- #1
ha9981
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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.
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"?
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"?