General

Inverse matrices are like inverses for numbers:

A A^-1 = A^-1 A = I

Note that .

The inverse only exists when the determinant of the matrix, |A|, is nonzero.

To get the inverses of small matrices, you could use the procedure of taking ``minors''. In index notation:

where A_ij is the matrix A after you remove the column and row of element a_ij. See the example problems.

Inverting products:

(AB)^-1 = B^-1 A^-1

Transposing and inversing commute: