If A and B are square matrices of the same order such that AB=BA, then – InterviewSolution

1.	If A and B are square matrices of the same order such that AB=BA, then prove by induction that ABn=BnA. Further, prove that (AB)n =AnBn for all n∈N.
Answer» If A and B are square matrices of the same order such that AB=BA, then prove by induction that A $B^{n}$ = $B^{n}$ A. Further, prove that $(A B)^{n}$ = $A^{n}$ $B^{n}$ for all $n \in N$ .

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