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If B ,C are square matrices of order na ...

If `B ,C` are square matrices of order `na n difA=B+C ,B C=C B ,C^2=O ,` then without using mathematical induction, show that for any positive integer `p ,A^(p+1)=B^p[B+(p+1)C]` .

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To solve the problem, we need to show that for any positive integer \( p \), the equation \[ A^{p+1} = B^p [B + (p+1)C] \] holds true, given the conditions \( A = B + C \), \( BC = CB \), and \( C^2 = O \) (the zero matrix). ...
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