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Question

If A is an orthogonal matrix of order 3 and B=123302250, 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
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B
2 only
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C
Both 1 and 2
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D
Neither 1 nor 2
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Solution

The correct option is C 1 only
Solution:
A is an orthogonal matrix.
A2=1
|A|2=1
|A|=±1
|AB|=±|B|
Now, |B|=123302250=47
|AB|=±47
And AB=373302250 and
BA=123302250
Since, ABBA
Hence, A is the correct option.

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