9.5 Inverses of Matrices

  • Find the inverse of a square matrix, if it exists.

  • Use inverses of matrices to solve systems of equations.

In this section, we continue our study of matrix algebra, finding the multiplicative inverse, or simply inverse, of a square matrix, if it exists. Then we use such inverses to solve systems of equations.

The Identity Matrix

Recall that, for real numbers, a·1=1·a=a; 1 is the multiplicative identity. A multiplicative identity matrix is very similar to the number 1.

Example

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