Wednesday, 5 June 2013

linear algebra - Prove if A is a square matrix and AB=ACRightarrowB=C, then A is invertible.



Prove: if A is a square matrix and AB=AC implies B=C, then A is invertible.




First year linear algebra, haven't gotten to determinants yet so the proof can't use determinants or anything beyond.



Edit: Solved, thanks.


Answer



Consider the equation: AX=0. We show X=0. Write: AX=A0X=0. Thus A is invertible.


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