(8 marks in total) (a) (4 marks) Let A and B be two n X n...

 

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(8 marks in total) (a) (4 marks) Let A and B be two n X n matrices such that A2 = 1, B2 = I and (AB) = I, where I is the nXn identity matrix. Prove that, in this case, AB = BA. (b) (4 marks) Give a counterexample using 3 X 3 matrices to show that the following statement is false: XY YX, for all n x n matrices X and Y (8 marks in total) (a) (4 marks) Let A and B be two n X n matrices such that A2 = 1, B2 = I and (AB) = I, where I is the nXn identity matrix. Prove that, in this case, AB = BA. (b) (4 marks) Give a counterexample using 3 X 3 matrices to show that the following statement is false: XY YX, for all n x n matrices X and Y