Suppose A and B be two non-singular matrices such that A B=B A^m, B^n=I and A^p=I, where I is an ...

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Suppose A and B be two non-singular matrices such that A B=B A^m, B^n=I and A^p=I, where I is an identity matrix.
The relation between m, n and p, is
(a) p=m n^2
(b) p=m^n-1
(c) p=n^m-1
(d) p=m^n-1

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