Solution
= Solution
A <triangular matrix> has <determinant> equal to the product of its diagonal entries. Since $L$ is a <unit lower triangular matrix>, $\det L=1$. Thus
$$
\boxed{\det A=\det L\det U=1\cdot(1\cdot4\cdot(-1))=-4.}
$$
Equivalently, the elimination used only row additions, which leave the <determinant> unchanged; there were no row swaps or row scalings to account for.