Inverse matrices are like inverses for numbers:

*A A ^{-1}* =

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:

Inverting products:

(*AB*)^{-1} = *B ^{-1}*

Transposing and inversing commute: