This is the question that I'm having trouble with:
I understand what the alternating and multilinear properties are, and I know that the determinant of the matrix is an alternating, multilinear function of the coloumns. But I don't understand the exact significance in this question.
I'm assuming that I cannot simply say that the LHS = det(A)det(B) = RHS ? Surely it must be more complicated than this?