Invent a $$4\times4$$ matrix and compute its determinant.
See development and solution
Development:
$$C=\left(\begin{matrix} 1 & 0 & 1 & 0 \\ 0 & 3 & 1 & -1 \\ 1 & 0 & 1 & 2 \\ 0 & 1 & 1 & 0 \end{matrix} \right)$$
$$det(C)=1\cdot det(B)+ 1\cdot\left|\begin{matrix} 0 & 3 & -1 \\ 1 & 0 & 2 \\ 0 & 1 & 0 \end{matrix} \right|=$$
$$1\cdot(-3)+1\cdot[0\cdot0\cdot0+1\cdot1\cdot(-1)+0\cdot2\cdot3-0\cdot0\cdot(-1)-1\cdot2\cdot0-0\cdot1\cdot3]=$$
$$=-3+(0-1+0-0-0-0)=-3-1=-4$$
Solution:
$$det(C)=-2$$.