Exercise 1

Consider the matrices $$A = \left[\begin{array}{rrr} 2 & 1 & 0 \\ -4 & -4 & 3 \\ 2 & 1 & -3 \\ \end{array}\right], \qquad B = \left[\begin{array}{rrrr} -2 & 3 & 0 & 0 \\ 0 & 4 & 2 & 0 \\ 4 & -6 & -1 & 2 \\ 0 & 4 & 2 & -3 \\ \end{array}\right]$$.

1. Find the determinants of $A$ and $B$ using row operations.

2. Now find the determinants of $A$ and $B$ using cofactor expansions to verify your results