Prove that if A is an invertible matrix and AB = BC then B = C. I thought the way to approach it was to use A^-1 on the equality AB=BC but then I got stuck. I can't get it so that B is on one side and C alone is on the other.(adsbygoogle = window.adsbygoogle || []).push({});

My Try:

AB = BC

A^-1 AB = A^-1 BC

IB = A^-1BC

Also why does B = C not contradict the statement that "the cancellation law doesn't hold for matrices"?

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# Prove that if A is an invertible matrix and AB = BC then B = C.

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