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Chapter 6: Q45E (page 309)

IfA is an invertible n脳n matrix, then A must commute with its adjoint, adj(A).

Short Answer

Expert verified

Therefore,

A鈰�adjA=adjA鈰�A

So, the given statement is true.

Step by step solution

01

Matrix Definition

Matrix is a setof numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are rows and columns, the matrix is said to be an 鈥� m by n鈥� matrix, written 鈥�m脳n.鈥�

02

To check whether the given condition is true or false

Ifis an invertible matrix, then

A-1=1detAadjA.

Then,

A鈰�adjA=A鈰�(detA)A-1A鈰�adjA=(detA)AA-1A鈰�adjA=(detA)IA鈰�adjA=(detA)A-1A

Therefore,

A鈰�adjA=adjA鈰�A

So, the given statement is true.

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Most popular questions from this chapter

There exist real invertible 3脳3 matrices A andSsuch that STAS=-A

Use Cramer's rule to solve the systems in Exercises 22 through 24.

22.|3x+7y=14x+11y=3|

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Question: Arguing geometrically, determine whether the following orthogonal transformations from鈩�3to鈩�3preserve or reverse orientation. See Exercise 20.
a. Reflection about a plane

b. Reflection about a line
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