Proof: If det(A) != 0 and AB = AC, then B = C

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We prove that if the determinant of a matrix A is nonzero and AB = AC, then we have that B = C. I hope this helps someone learning linear algebra.

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One might note that by imposing that det(A) =/= 0, we are forming a group, and the statement AB = AC => B = C is a general property of groups. Thus, this proof and concept are highly generalizable (its not actually about matrices _per se_ in its essence).

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