S swiftshift May 2010 7 0 May 13, 2010 #1 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.

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.

undefined MHF Hall of Honor Mar 2010 2,340 821 Chicago May 13, 2010 #2 swiftshift said: 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. Click to expand... I'll address b (i). Write AABB. Do you see how to manipulate that to obtain BBAA, using what we've been given? Reactions: HallsofIvy

swiftshift said: 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. Click to expand... I'll address b (i). Write AABB. Do you see how to manipulate that to obtain BBAA, using what we've been given?

Z zzzoak Mar 2010 280 122 May 13, 2010 #3 AB=I Multiply left C*: CAB=C (CA)B=C as CA=I we get B=C. Reactions: HallsofIvy and swiftshift