What method is used to find the determinant of this $4 \times 4$ matrix?

Question

This is a pre-solved example in my book, I don't understand how they solved it. What method is used?

Find the determinant of $A = \begin{bmatrix} 0 & 1 & 0 & 2\\[0.3em] -1 & 1 & 1 & 3\\[0.3em] 0 & 0 & 0 & 1\\ 1 & -2 & 0 & 1 \end{bmatrix}$

$det(A)=-1\times det \begin{bmatrix} -1 & 1 & 3\\[0.3em] 0 & 0 & 1 \\[0.3em] 0 & 0 & 1 \\ \end{bmatrix} -2\times det \begin{bmatrix} -1 & 1 & 1\\[0.3em] 0 & 0 & 0 \\[0.3em] 1 & -2 & 0 \\ \end{bmatrix}$
$=-1\times 1+0$
$=-1$

Answer 1

The Laplace expansion is used to calculate the given determinant: we expand along the first row.