Answer
$-1$
Work Step by Step
Expanding down the first column, we see that the first two cofactors vanish, leaving the determinant equal to $1\begin{vmatrix}0&1\\1&0\end{vmatrix}=1(0-1)=-1$. Note that Theorem 2 does not apply, as the elementary matrix given does not satisfy the definition of a triangular matrix.
