College Algebra Matrices
Inverses of Matrices
   Concepts 1

Definition 
.
If A is an n x n matrix and if there exists an n x n matrix B such that AB=BA=In, we say that B is the multiplicative inverse, or simply the inverse, of A.
The multiplicative inverse of A is written B=A-1.
A matrix that has a multiplicative inverse is said to be nonsingular; otherwise, it is singular.

Statement 
.
An n x n matrix A is nonsingular if and only if |A| is not equal to zero.

Theorem 
.
Let
If the determinant , then the multiplicative inverse of A is
where Aij is the cofactor of the element aij of the determinant |A|.

Example 1. Find inverse of the matrix:
 .

Solution











Check:


Copyright © 1998-2001 MathAid, LLC. All rights reserved.