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If A and B are squre 3xx3 such that A is...

If A and B are squre `3xx3` such that A is an orthogonal matrix and B is a skew- symmetrix matrix , then which of the following statement is true?

A

`abs(AB)=1`

B

`abs(AB)=0`

C

`abs(AB)=-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
A an orthogonal matrix `rArr absA=pm1`
B a skew-symmetric matrix of odd order `rArr absB=0`
`:. abs(AB)=absAabsBrArr abs(AB)=(pm1)xx0=0`.
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