If \( B, C \) are \( n \) rowed square matrices and if \( A=B+C, B ...

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If \( B, C \) are \( n \) rowed square matrices and if \( A=B+C, B C=C B, C^{2}=O \), then show that for every \( n \in N, A^{n+1}=B^{n}(B+(n+1) C) \).
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