Thursday, 27 April 2017

Explaining invertible matrices with linear transformations

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 RnRn, explain why both A and B must be invertible.



So I think it has to do with xAx and xBx 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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