A matrix has an inverse if and only if its determinant does not equal 0. Determine whether the given matrix has an
inverse.
-$$\left[ \begin{array} { r r }
7 & - 4 \
- 7 & 5
\end{array} \right]$$
A) No
B) Yes

Question

A matrix has an inverse if and only if its determinant does not equal 0. Determine whether the given matrix has an
inverse.
-$$\left[ \begin{array} { r r } 
7 & - 4 \
- 7 & 5
\end{array} \right]$$
A) No
B) Yes

Quizplus · Accepted Answer

The determinant of the matrix is $7(5) - (-4)(-7) = 35 - 28 = 7$, which is not equal to 0. Therefore, the matrix has an inverse.

A Matrix Has an Inverse If and Only If Its [7−4−75]\left[ \begin{array} { r r } 7 & - 4 \\- 7 & 5\end{array} \right][7−7​−45​]

A Matrix Has an Inverse If and Only If Its $\left[ \begin{array} { r r } 7 & - 4 \\- 7 & 5\end{array} \right]$