[Math] Finding determinants by inspection

determinantlinear algebra

I'm supposed to "use properties of determinants to evaluate the determinant by inspection" on this matrix:
$$\begin{bmatrix} 4 & 1& 3\\
-2 & 0 &-2 \\
5 & 4 & 1\end{bmatrix}.$$

I don't see anything (zero rows, ways to transform the matrix) that would make it immediately obvious what the determinant is. What am I missing?

Best Answer

Take the third column away from the first. This leaves column 1 and 2 equal, thus the determinant = 0