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

Step 1. Given Information

A square matrix A which is nonsingular also

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

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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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

Step by step solution

Step 1. Given Information

Step 2. Calculation

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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

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Probability and Statistics

Geometry

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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.