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If A is an orthogonal matrix of order 3 ...

If A is an orthogonal matrix of order 3 and B = `[{:(1,2,3),(-3,0,2),(2,5,0):}]`, then which of the following is/are correct ?
1. `|AB|= +- 47`
2. AB = BA
Select the correct answer using the code given below :

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
A
The determinent of a orthogonal matrix is always `pm1`
`|A|= pm1`
`B=[(1,2,3),(-3,0,2),(2,5,0)]`
`|B|=-10-2(-4)+3(-15)`
`=-47`
`|AB|=|A||B|`
`=(pm1)(-47)`
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