This should be 2*2 matrix, otherwise it would not make any sense.

So, multiplying A by A, we get A^2 = [Cos2a -Sin2a  Sin2a Cos2a]. Doing the same 32 times, you will get A^32 = [Cos32a -Sin32a Sin32a Cos32a]

Comparing the given data with this, we get cos32a = 0 and sin32a = 0 and -sin32a = -1 which seems to be invalid as it is saying that sin32a = 0 = 1 which is not possible. So, no such a exists.