Hello everyone...I'm studying for a midterm exam and I'm having a lot of trouble understanding this particular excercise:

Suppose matrices A and C have size n x n and matrices X, B and D have size n x 1.

1) True or False: AA -¹ A -¹ AX = X

2) True or False: If AX = B, then X = BA -¹

3) True or False: If XC = D, then X = DC -¹

I honestly do not even know where to begin with this...I'd really appreciate help figuring this problem out.

Thanks in advance.