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Let G be the set of all 2x2 invertible matrices whose columns add up to 1. So, G is the set of all matrices A=[abcd] such that a+b=1 and c+d=1. Prove that G is a group under matrix multiplication.
So I know I have to prove closeness, associativity (which I've done), identity element, and being invertible everywhere, which I'm not sure how to use another matrix B to do so.
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