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Let A be a matrix of order 3, such that ...

Let A be a matrix of order 3, such that `A^(T)A=I`. Then find the value of det. `(A^(2)-I)`.

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The correct Answer is:
0
det. `(A^(2)-I)=` det. `(A A-A^(T)A)`
= det. `[(A-A^(T))A]`
=det. `(A-A^(T))` det. A
Now, `A-A^(T)` is skew-symmetric matrix.
`:.` dte. `(A-A^(T))=0`
`implies` det. `(A^(2)-I)=0`
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