Inverse Matrix

The inverse matrix, A^-1, of the matrix A is a matrix such that AA^-1=A^-1A=I (where I is the identity matrix).

It can be shown that:

If for the matrices A and B, AB = BA = I, then the matrix A is said to be invertible and it has an inverse matrix (in this case B). Otherwise we say that A is non-invertible. Notice also that the expression ad-bc is called the determinant of the matrix A. This is written as detA, and the determinant of A, a 2x2 matrix (2x2 is read as: two by two) is given by:

detA = |A| = = ad-bc