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Matrices

發問:

A, B and C are three 3 x 3 matrices. If AB = CB, then A = C, is this true ? Please prove. If this is not true, under what condition that this is true ?

最佳解答:

Not true. If A= (1 1) (1 1) C= (1 0) (1 1) B= (0 0) (0 0) Obviously, AB = CB = zero matrix, but A <> C. However if B is non singular, the claim is true. Proof: AB = CB, then AB*(B inverse) = CB*(B inverse), then A*I = C*I, then A=C.

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