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Question

If A is a square matrix of order 3 such that AAT=I and
|A|=1, then |AI|=

A
0
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B
1
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C
1
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D
none of these
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Solution

The correct option is A 0
A is a square matrix of order 3 such that AAT=Iand|A|=1
AT=A1ATA=I
(AI)T=ATIT=ATI
ATATA=AT(IA)
taking dterminant on both sides,
|(AI)T|=|AT(IA)|
|(AI)|=|A||IA|
|(AI)|=|(AI)|
|AI|=0

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