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Chapter 6: Q47E (page 309)

IfA andB are orthogonaln脳n matrices such thatdetA=detB=1, then matricesA and Bmust commute.

Short Answer

Expert verified

Therefore,

AB鈮�BA

So, the given statement is false.

Step by step solution

01

Orthogonal Matrix Definition

A square matrix with real numbers or elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix.

Or we can say, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix

02

To check whether the given condition is true or false

For example,

A=010-100001

B=1000010-10

Clearly, bothA andB are orthogonal matrices, anddetA=detB=1.

However,

AB=001-1000-10

AB鈮�010001100

AB鈮�BA.

So, the given statement is false.

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