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If A is a non singular square matrix whe...

If A is a non singular square matrix where `B=A^T and A+B^2=I` such that `A^3+I=kA` then find the value of k.

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`B=A^T`
`|A|!=0`
`A^3+I=A*A A+I`
`=A*(B^T)^2+I`
`=A*(B^2)^T+I`
`=A*(I^T-A^T)+I`
`=A*(I-A^T)+I`
`=A_I-A A^T+I`
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