If A, B, and C are all square matrices of the same size, show that AB commutes with C if A and B both commute with C. All I know is AC = CA BC = CB But I don't know what to do with that information to prove this.
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Originally Posted by paulrb If A, B, and C are all square matrices of the same size, show that AB commutes with C if A and B both commute with C. All I know is AC = CA BC = CB But I don't know what to do with that information to prove this. Since $\displaystyle AC = CA\;\;\Rightarrow\;\;ACB = CAB\;\;\Rightarrow\;\; ABC=CAB$.
Thanks, that's a lot easier than I thought. I guess I was thinking too hard.
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