Question 1: Let A be a k x k matrix and let B be an (n-k) x (n-k) matrix. Let

$\displaystyle E= \begin{array}{cc} I_k & 0 \\ 0 & B\end{array}$

Show that det(E) = det(B)

My attempt: $\displaystyle det(E)=det(BI_k) - det(00)=det(B)det(I_k)=det(B)*1=det(B)$

I'm not sure this is correct, as I don't know the rules for finding the determinant of a matrix populated itself with matrices. Can anyone point me in the right direction?

Thanks,

CP