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Question

If nth order square matrix A is a orthogonal, then adj(adjA) is


A

always -1 if nis even

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B

always 1 if nis odd

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C

always 1

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D

none of these

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Solution

The correct option is B

always 1 if nis odd


Explanation for the correct option

Given that nth order square matrix A is a orthogonal

AT=A-1A.AT=I

We know that the value of the determinant of an orthogonal matrix is ±1

A=±1

We know that adjadjA=An-12

If nis odd then n-12 is even.

Aeven=±1even=1always

Hence the correct option is option(B) i.e. always 1 if nis odd


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