College Algebra Matrices
Inverses of Matrices Concepts 1

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

|  |  | Theorem |  |
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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:

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