Question

In the following exercises, evaluate the determinate of each square matrix.

$\left[\begin{array}{cc}-3& 5\\ 0& -4\end{array}\right]$

Short answer

The value of the determinant is$12.$

Step-by-step solution

Step 1. Given information  

The given square matrix is

$\left[\begin{array}{cc}-3& 5\\ 0& -4\end{array}\right]$

We have to evaluate the determinate of a given square matrix.

Step 2. To find the determinant, multiply the diagonals of the matrix and then subtract them. 

The determinant of the matrix is

$$\begin{gathered} =(-3)(-4)-\left(0\right)\left(5\right) \\ =\left(12\right)-0 \\ =12 \end{gathered}$$