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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 5 (page 755)

Suppose that A is a square n by n matrix that is nonsingular.
The matrix B such that AB = BA = In is called the__________
of the matrix A.

Short Answer

Expert verified

Inverse.

Step by step solution

01

Step 1. Given Information

A square matrix A which is nonsingular also

$A B = B A = I_{n}$

02

Step 2. Calculation

$C o n s i d e r, A = [\begin{matrix} 3 & 1 \\ 1 & - 2 \end{matrix}] B = [\begin{matrix} \frac{2}{7} & \frac{1}{7} \\ \frac{1}{7} & - \frac{3}{7} \end{matrix}] A B = [\begin{matrix} 3 & 1 \\ 1 & - 2 \end{matrix}] [\begin{matrix} \frac{2}{7} & \frac{1}{7} \\ \frac{1}{7} & - \frac{3}{7} \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

thus, $A A^{- 1} = I_{n}$

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