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The inverse of a matrix is another matrix which, when multiplied
by the first matrix, yields the unit matrix (a matrix with all
zeroes except 1's down the diagonal).

(22) 
In the general case, the inverse may be written

(23) 
where
is the transpose of the matrix of cofactors
. For example:

(24) 
Clearly, there are major problems in finding the inverse of a matrix
if it has a determinant equal to zero, since the formula for
involves dividing by the determinant. In such cases, we say that
is singular and has no inverse.
David Sherrill
20060815