Suppose that A and B are square matrices and that AB is invertible. Using the interpretation of multiplication by A (or B) as a linear transformation from Rn→Rn, explain why both A and B must be invertible.
So I think it has to do with x↦Ax and x↦Bx being onto and one-to-one and then using the invertible matrix theorem, but I don't quite understand how to answer this precisely.
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