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If a, b, and c are integers, then number...

If a, b, and c are integers, then number of matrices `A=[(a,b,c),(b,c,a),(c,a,b)]` which are possible such that `A A^(T)=I` is _______.

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The correct Answer is:
6
`A A^(T)=I`
`:. A^(2)+b^(2)+c^(2)=1` and `ab+bc+ca=0`
This is possible when
(i) `a= pm 1, b=c=0`
(ii) `a=0, b= pm 1, c=0`
(iii) `a=0, b=0, c= pm 1`
So, there are six such matrices A.
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