Similarity (conjugate) math problem

franky2727

my question is what is meant by saying that A and B are similar where A and B are nxn matrices with entries in field F, also show that is A~B then A^2~b^2

first bit i have the definition for A~B is they are nxn matrices in the same field and there exists a non-singular square matrix P such that B=P^-1AP

however i have no ideas about the second part, its only revision not homework so could someone please define this for me? thanks

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Defennder

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Re: similarity(conjugate)

A matrix A is similar to matrix B (both are n x n matrices) if there exists an invertible nxn matrix P such that A=P^(-1)BP. Use this definition and that of A to show that A^2 is similar to B^2.

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