Let M be a nxn matrix and A is a mxm and C is kxk square matrix.

If

where O is made of all entries equal to zero and B is any matrix.

Prove det(M) = det(A) det(C)

the only way i can think of it is to expand about the first column but it seems way too tedious. and we only have learnt the definition of determinant and Cramer's rule.