diff --git a/bed-and-breakfast.cabal b/bed-and-breakfast.cabal
--- a/bed-and-breakfast.cabal
+++ b/bed-and-breakfast.cabal
@@ -1,5 +1,5 @@
 Name:           bed-and-breakfast
-Version:        0.2
+Version:        0.2.1
 Synopsis:       Efficient Matrix operations in 100% Haskell.
 Description:    Efficient Matrix operations in 100% Haskell.
                 .
@@ -27,7 +27,11 @@
                 [@v0.2@] A little bit more documentation. Also moved some
                     functions (@isXXX@) away from the type class @MatrixElement@.
                     Properly flagged the package as experimental (was
-                    improperly copied as @stable@, copied form a template).
+                    improperly marked as @stable@, copied form a
+                    template).
+                .
+                [@v0.2.1@] Added @cofactors@, @adjugate@, @minor@, and
+                    @minorMatrix@.
 
 License:        MIT
 License-File:   LICENSE
diff --git a/src/Numeric/Matrix.hs b/src/Numeric/Matrix.hs
--- a/src/Numeric/Matrix.hs
+++ b/src/Numeric/Matrix.hs
@@ -38,61 +38,17 @@
     Matrix,
 
     MatrixElement (..),
- 
-    -- * Matrix property and utility functions.
 
-    -- | Joins two matrices horizontally.
-    --
-    -- > 1 2 3     1 0 0      1 2 3 1 0 0
-    -- > 3 4 5 <|> 2 1 0  ->  3 4 5 2 1 0
-    -- > 5 6 7     3 2 1      5 6 7 3 2 1
+    -- * Matrix property and utility functions.
     (<|>),
-
-    -- | Joins two matrices vertically.
-    --
-    -- > 1 2 3     1 0 0      1 2 3
-    -- > 3 4 5 <-> 2 1 0  ->  3 4 5
-    -- > 5 6 7     3 2 1      5 6 7
-    -- >                      1 0 0
-    -- >                      2 1 0
-    -- >                      3 2 1
     (<->),
-
-    -- | Scales a matrix by the given factor.
-    -- 
-    -- > scale s == map (*s)
     scale,
 
-    -- * Matrix properties
-
-    -- | Check whether the matrix is an identity matrix.
-    --
-    -- > 1 0 0
-    -- > 0 1 0
-    -- > 0 0 1 (True)
+    -- ** Matrix properties
     isUnit,
-
-    -- | Check whether the matrix consists of all zeros.
-    --
-    -- > isZero == all (== 0)
     isZero,
-
-    -- | Checks whether the matrix is a diagonal matrix.
-    --
-    -- > 4 0 0 0
-    -- > 0 7 0 0
-    -- > 0 0 3 0
-    -- > 0 0 0 9 (True)
     isDiagonal,
-
-    -- | Checks whether the matrix is empty.
-    --
-    -- > isEmpty m = numCols == 0 || numRows == 0
     isEmpty,
-
-    -- | Checks whether the matrix is a square matrix.
-    --
-    -- > isSquare == uncurry (==) . dimensions
     isSquare
     
 ) where
@@ -123,17 +79,23 @@
 
 data family Matrix e
 
-data instance Matrix Int = IntMatrix !Int !Int (Array Int (UArray Int Int))
+data instance Matrix Int
+    = IntMatrix !Int !Int (Array Int (UArray Int Int))
 
-data instance Matrix Float = FloatMatrix !Int !Int (Array Int (UArray Int Float))
+data instance Matrix Float
+    = FloatMatrix !Int !Int (Array Int (UArray Int Float))
 
-data instance Matrix Double = DoubleMatrix !Int !Int (Array Int (UArray Int Double))
+data instance Matrix Double
+    = DoubleMatrix !Int !Int (Array Int (UArray Int Double))
 
-data instance Matrix Integer = IntegerMatrix !Int !Int (Array Int (Array Int Integer))
+data instance Matrix Integer
+    = IntegerMatrix !Int !Int (Array Int (Array Int Integer))
 
-data instance Matrix (Ratio a) = RatioMatrix !Int !Int (Array Int (Array Int (Ratio a)))
+data instance Matrix (Ratio a)
+    = RatioMatrix !Int !Int (Array Int (Array Int (Ratio a)))
 
-data instance Matrix (Complex a) = ComplexMatrix !Int !Int (Array Int (Array Int (Complex a)))
+data instance Matrix (Complex a)
+    = ComplexMatrix !Int !Int (Array Int (Array Int (Complex a)))
 
 instance Typeable a => Typeable (Matrix a) where
     typeOf x = mkTyConApp (mkTyCon3 "bed-and-breakfast"
@@ -171,6 +133,11 @@
 
 
 (<|>) :: MatrixElement e => Matrix e -> Matrix e -> Matrix e
+-- ^ Joins two matrices horizontally.
+--
+-- > 1 2 3     1 0 0      1 2 3 1 0 0
+-- > 3 4 5 <|> 2 1 0  ->  3 4 5 2 1 0
+-- > 5 6 7     3 2 1      5 6 7 3 2 1
 m1 <|> m2 = let m = numCols m1
                 n1 = numRows m1
                 n2 = numRows m2
@@ -180,6 +147,14 @@
                     else (if i > n1 then 0 else m1 `at` (i,j))
 
 (<->) :: MatrixElement e => Matrix e -> Matrix e -> Matrix e
+-- ^ Joins two matrices vertically.
+--
+-- > 1 2 3     1 0 0      1 2 3
+-- > 3 4 5 <-> 2 1 0  ->  3 4 5
+-- > 5 6 7     3 2 1      5 6 7
+-- >                      1 0 0
+-- >                      2 1 0
+-- >                      3 2 1
 m1 <-> m2 = let m = numRows m1
                 n1 = numCols m1
                 n2 = numCols m2
@@ -189,17 +164,44 @@
                     else (if j > n1 then 0 else m1 `at` (i,j))
 
 scale :: MatrixElement e => Matrix e -> e -> Matrix e
+-- ^ Scales a matrix by the given factor.
+-- 
+-- > scale s == map (*s)
 scale m s = map (*s) m
 
 
 isUnit, isDiagonal, isZero, isEmpty, isSquare :: MatrixElement e => Matrix e -> Bool
 
+-- | Check whether the matrix consists of all zeros.
+--
+-- > isZero == all (== 0)
 isZero = all (== 0)
+
+-- | Check whether the matrix is an identity matrix.
+--
+-- > 1 0 0
+-- > 0 1 0
+-- > 0 0 1 (True)
 isUnit m = isSquare m && allWithIndex (uncurry check) m
     where check = \i j e -> if i == j then e == 1 else e == 0
+
+-- | Checks whether the matrix is empty.
+--
+-- > isEmpty m = numCols == 0 || numRows == 0
 isEmpty m = numRows m == 0 || numCols m == 0
+
+-- | Checks whether the matrix is a diagonal matrix.
+--
+-- > 4 0 0 0
+-- > 0 7 0 0
+-- > 0 0 3 0
+-- > 0 0 0 9 (True)
 isDiagonal m = isSquare m && allWithIndex (uncurry check) m
     where check = \i j e -> if i /= j then e == 0 else True
+
+-- | Checks whether the matrix is a square matrix.
+--
+-- > isSquare == uncurry (==) . dimensions
 isSquare m = let (a, b) = dimensions m in a == b
 
 
@@ -272,6 +274,11 @@
     rank      :: Matrix e -> e
     trace     :: Matrix e -> [e]
 
+    minor :: MatrixElement e => Matrix e -> (Int, Int) -> e
+    cofactors :: MatrixElement e => Matrix e -> Matrix e
+    adjugate :: MatrixElement e => Matrix e -> Matrix e
+    minorMatrix :: MatrixElement e => Matrix e -> (Int, Int) -> Matrix e
+
     -- Applies a function on every component in the matrix.
     map :: MatrixElement f => (e -> f) -> Matrix e -> Matrix f
 
@@ -307,11 +314,20 @@
     dimensions m = case toList m of [] -> (0, 0)
                                     (x:xs) -> (length xs + 1, length x)
 
---    adjugate = transpose . cofactors
+    adjugate = transpose . cofactors
     transpose = fromList . L.transpose . toList
     trace = select (uncurry (==))
     inv _ = Nothing
 
+    minorMatrix m (i,j) = matrix (numRows m - 1, numCols m - 1) $
+                \(i',j') -> m `at` (if i' >= i then i' + 1 else i',
+                                    if j' >= j then j' + 1 else j')
+
+    minor m = det . minorMatrix m
+
+    cofactors m = matrix (dimensions m) $
+       \(i,j) -> fromIntegral ((-1 :: Int)^(i+j)) * minor m (i,j)
+
     map f = mapWithIndex (const f)
     all f = allWithIndex (const f)
     any f = anyWithIndex (const f)
@@ -344,9 +360,8 @@
     row i      (IntMatrix _ _ arr) = _row i arr
     col j      (IntMatrix _ _ arr) = _col j arr
     toList     (IntMatrix _ _ arr) = _toList arr
-    inv _ = Nothing
     det        (IntMatrix m n arr) = if m /= n then 0 else runST (_det thawsUnboxed arr)
-    rank = undefined -- runST (_rank thawsBoxed arr)
+    rank       (IntMatrix _ _ arr) = runST (_rank thawsBoxed arr)
 
 instance MatrixElement Integer where
     matrix   = _matrix IntegerMatrix
@@ -357,9 +372,8 @@
     row i      (IntegerMatrix _ _ arr) = _row i arr
     col j      (IntegerMatrix _ _ arr) = _col j arr
     toList     (IntegerMatrix _ _ arr) = _toList arr
-    inv _ = Nothing
     det        (IntegerMatrix m n arr) = if m /= n then 0 else runST (_det thawsBoxed arr)
-    rank = undefined -- runST (_rank thawsBoxed arr)
+    rank       (IntegerMatrix _ _ arr) = runST (_rank thawsBoxed arr)
 
 instance MatrixElement Float where
     matrix   = _matrix FloatMatrix
@@ -370,11 +384,11 @@
     row i      (FloatMatrix _ _ arr) = _row i arr
     col j      (FloatMatrix _ _ arr) = _col j arr
     toList     (FloatMatrix _ _ arr) = _toList arr
+    det        (FloatMatrix m n arr) = if m /= n then 0 else runST (_det thawsUnboxed arr)
+    rank       (FloatMatrix _ _ arr) = runST (_rank thawsBoxed arr)
     inv        (FloatMatrix m n arr) = if m /= n then Nothing else
                                          let x = runST (_inv unboxedST arr)
                                          in maybe Nothing (Just . FloatMatrix m n) x
-    det        (FloatMatrix m n arr) = if m /= n then 0 else runST (_det thawsUnboxed arr)
-    rank       (FloatMatrix _ _ arr) = runST (_rank thawsBoxed arr)
 
 instance MatrixElement Double where
     matrix   = _matrix DoubleMatrix
@@ -415,7 +429,7 @@
     row i      (ComplexMatrix _ _ arr) = _row i arr
     col j      (ComplexMatrix _ _ arr) = _col j arr
     toList     (ComplexMatrix _ _ arr) = _toList arr
-    inv        (ComplexMatrix _ _ _) = Nothing
+--    inv        (ComplexMatrix _ _ _) = Nothing
 --if m /= n then Nothing else
 -- Just $ ComplexMatrix m n $ runST (_inv boxedST arr)
     det        (ComplexMatrix m n arr) = if m /= n then 0 else runST (_det thawsBoxed arr)
@@ -567,7 +581,7 @@
 
       else return Nothing
 
-_rank :: (IArray a e, MArray (u s) e (ST s), Fractional e, Eq e)
+_rank :: (IArray a e, MArray (u s) e (ST s), Num e, Division e, Eq e)
       => (Array Int (a Int e) -> ST s [(u s) Int e])
       -> Array Int (a Int e)
       -> ST s e
@@ -586,7 +600,7 @@
                 a_kj <- readArray a_k j
                 a_ik <- readArray a_i k
                 a_kk <- readArray a_k k
-                writeArray a_i j (a_ij - a_kj * (a_ik / a_kk))
+                writeArray a_i j (a_ij - a_kj * (a_ik `divide` a_kk))
             writeArray a_i k 0
         read a k k