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

Is the following true for matrices?

Hypotesis:

AB = AC

A != 0(zero matrix)

Thesis:

B=C

3. The attempt at a solution

AB = AC

AB - AC = 0(zero matrix)

AB - AC = A(B-C)// using the following property: A(B+C) = AB + AC iff A is mn matrix and BC are np matrices

A(B-C) = 0 <=> B=CbecauseA != 0

QED

There is something wrong because there are matrices where AB = AC and B != C.

Where is my mistake?

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# Need help to find my mistake in a simple proof of a matrix algebra proposition.

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