(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let m < n. Let A be an n × m matrix, and let B be an m × n matrix. Prove that AB /= In .

2. Relevant equations

3. The attempt at a solution

since m<n, the reduced form of matrix B will have free variables.

I know that if A and B are invertible matrices, AB will be as well but does the converse also hold?

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# Linear algebra proof - inverses

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