Question

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

$\left[\begin{array}{cc}6& -2\\ 3& -1\end{array}\right]$

Short answer

The value of the determinant is 0.

Step-by-step solution

Step 1. Given information

The given square matrix is

$\left[\begin{array}{cc}6& -2\\ 3& -1\end{array}\right]$

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

$$\begin{gathered} =\left(6\right)(-1)-\left(3\right)(-2) \\ =(-6)-(-6) \\ =-6+6 \\ =0 \end{gathered}$$