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Question

The total number of matrices
A=02y12xy12xy1,(x,yR, xy)

for which ATA=3I3 is :

A
2
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B
4
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C
6
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D
3
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Solution

The correct option is B 4
A=02y12xy12xy1

AT=02x2x2yyy111

Now, ATA=3I3
02x2x2yyy11102y12xy12xy1=300030003

8x20006y20003=300030003

8x2=3x=±322
and 6y2=3y=±12

Therefore, 4 such matrices are possible.


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