Linear algebra, matrices, and you

[TBag]

So yes, here is a math problem I'm rather curious about. In this situation, I'm guessing that A is just an identity matrix of n x n, would that be correct? If so, how would one go about proving it?



Also, for the true or false questions I got
1 true
2 false
3 I'm pretty sure this one is true, because if C = A^-1, and B = C^-1, therefore A=B, but I'm not sure I'll work one out and then edit my answer in
4 True

edit - I did number 3 with the matrix
1 2
3 4
And it proved the statement true. Is there any instance where it wouldn't?