Let A and B be two square matrices with the same dimensions. If the result of multiplying A by B from either side is the identity matrix I, then B is the multiplicative inverse of A.

The multiplicative inverse of a matrix A is usually denoted A^(- 1).

Example

Consider two 3* 3 matrices. A= 1 & 0 & 2 - 2 & 1 & 1 - 1 & 1 & 2 B= - 1 & - 2 & 2 - 3 & - 4 & 5 1 & 1 & - 1 It can be shown that B is the multiplicative inverse of A by calculating the products A* B and B* A. First, the product A* B is calculated. Next, the product B* A is calculated. Since A* B=I and B* A=I, B is the multiplicative inverse of A and B=A^(- 1).