A matrix has an inverse if and only if its determinant does not equal 0. Determine whether the given matrix has an
inverse.
-$$\left[ \begin{array} { r r }
8 & 3 \
- 16 & - 6
\end{array} \right]$$
A) Yes
B) No

Question

A matrix has an inverse if and only if its determinant does not equal 0. Determine whether the given matrix has an
inverse.
-$$\left[ \begin{array} { r r } 
8 & 3 \
- 16 & - 6
\end{array} \right]$$
A) Yes
B) No

Quizplus · Accepted Answer

The determinant of the matrix is calculated as $8(-6) - 3(-16) = -48 + 48 = 0$. Since the determinant equals 0, the matrix does not have an inverse.

A Matrix Has an Inverse If and Only If Its [83−16−6]\left[ \begin{array} { r r } 8 & 3 \\- 16 & - 6\end{array} \right][8−16​3−6​]

A Matrix Has an Inverse If and Only If Its $\left[ \begin{array} { r r } 8 & 3 \\- 16 & - 6\end{array} \right]$