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Let A ,B be two matrices such that they ...

Let `A ,B` be two matrices such that they commute. Show that for any positive integer `n ,` `A B^n=B^n A`

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To show that if matrices \( A \) and \( B \) commute, then for any positive integer \( n \), \( A B^n = B^n A \), we can use mathematical induction. Here is the step-by-step solution: ### Step 1: Base Case We start with the base case where \( n = 1 \). \[ A B^1 = A B \] ...
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