Find the determinant of A find the determinant of A using only determinant properties 
$$
    A=\begin{bmatrix}
    1 & 3 & -4   \\
    -2 & 1 & 2 \\
    -9 & 15 & 0  \\
    \end{bmatrix}
$$

Row reduction does not change the determinant:
$$
\begin{bmatrix} 1 & 3 & -4 \\ -2 & 1 & 2 \\ -9 & 15 & 0 \\ \end{bmatrix}
\to
\begin{bmatrix} 1 & 3 & -4 \\ 0 & 7 & -6 \\ 0 & 42 & -36 \\ \end{bmatrix}
\to
\begin{bmatrix} 1 & 3 & -4 \\ 0 & 7 & -6 \\ 0 & 0 & 0\\ \end{bmatrix}
$$
The determinant is zero because the last matrix has a row of zeros.
