a) A, B and C are n x n matrices such that AB= I and CA = I. show that B = C. b) A and B are n x n matrices that commute i) show that A^2 and B^2 commute. ii) Give a generalization of this result.
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Originally Posted by swiftshift a) A, B and C are n x n matrices such that AB= I and CA = I. show that B = C. b) A and B are n x n matrices that commute i) show that A^2 and B^2 commute. ii) Give a generalization of this result. I'll address b (i). Write AABB. Do you see how to manipulate that to obtain BBAA, using what we've been given?
AB=I Multiply left C*: CAB=C (CA)B=C as CA=I we get B=C.
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