Proving that matrices commute

May 2010
7
0
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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MHF Hall of Honor
Mar 2010
2,340
821
Chicago
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?
 
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