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If A and B are two matrices of order 3 s...

If A and B are two matrices of order 3 such that `AB=O` and `A^(2)+B=I`, then tr. `(A^(2)+B^(2))` is equal to ________.

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The correct Answer is:
3
`A^(2)+B=I`
`:. A^(2)B+B^(2)=B`
`implies B^(2)=B`
So, from (1), we get
`A^(2)+B^(2)=I`
`implies` tr. `(A^(2)+B^(2))=3`
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