Question

linear algebra: basis for W-perp?

Let V be the Euclidean space of all 2x2 matrices with the inner product defined by (A, B) = Tr((B^T)A), where Tr is the trace function. Let W= span{[1 -1; 2 3], [1 2; 0 -1]. Find a basis for W-perp.

Answer: {[-4/3 2/3; 1 0], [-5/3 4/3; 0 1]

How am I supposed to solve this? Can someone help me? do you have to combine the spanning vectors and row reduce it?