Question

Let A and B be 2×2 matrices, and assume that
AB = I, where I is the identity matrix. Select ALL statements
below which must be true.
• A. (BCA)2 = BC2A for any 2×2 matrix C
• B. ACB =C for any 2×2 matrix C
• C. A = B
• D. If BX = 0, then X = 0
• E. None of the above

Answer 1

Any idea which might be true or false?

Answer 2

my answer is A and D

Answer 3

thats correct :)

Answer 4

what about others?

Answer 5

They are false for sure. Since matrix multiplication is not commutative, B is false in general. For C, a counter example would do. It should be easy to find two by two matrices such that AB = I but A doesnt equal B.

Answer 6

could u give an example of two matrices

Answer 7

Sure, lets see....

Answer 8

thanks a million dude