## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 10 - 10.3 - The Inverse of a Square Matrix - 10.3 Exercises - Page 734: 5

#### Answer

B is the inverse of A.

#### Work Step by Step

When there is an inverse of a matrix $A A^{-1}$ = I (the Identity Matrix) AB = $\begin{bmatrix} 2(3) + 1(-5) & 2(-1) + 1(2) \\ 5(3) +3(-5) & (5)(-1) + 3(2)\\ \end{bmatrix}$ = $\begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}$ Since AB equals the identity matrix, B is the inverse of A.

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