7. (6 points)

a. (3 points) Let $B = \begin{bmatrix} 1 & -1 & 0 & 2 \\ 0 & 0 & 3 & 3 \\ 2 & 1 & 0 & 0 \\ 1 & 1 & 2 & 2 \end{bmatrix}$. Compute $\det(B)$.

b. (3 points) Let $Q$ be an orthogonal matrix. Show that $\det(Q)$ is either $1$ or $-1$.