Let A and B be n*n matrices and let their product AB be invertible. Prove A and B are invertible
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Originally Posted by I-Think Let A and B be n*n matrices and let their product AB be invertible. Prove A and B are invertible Let C be the inverse of AB, then C(AB) = (AB)C = I. Now use associativity in the above expression. do you see it?
Another way to see why it "should be" true is to consider the identity det(AB)=det(A)det(B). Isomorphism's answer is definitely more straightforward, though.
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