Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r }
0 & - 5 \
- 2 & 2
\end{array} \right]$$
A)
$$\left[ \begin{array} { r r }
- \frac { 1 } { 5 } & \frac { 1 } { 2 } \
\frac { 1 } { 5 } & 0
\end{array} \right]$$

B)
$$\left[ \begin{array} { c c }
- \frac { 1 } { 5 } & 0 \
- \frac { 1 } { 5 } & - \frac { 1 } { 2 }
\end{array} \right]$$

C)

$$\left[ \begin{array} { r r }
0 & - \frac { 1 } { 2 } \
- \frac { 1 } { 5 } & - \frac { 1 } { 5 }
\end{array} \right]$$

D)

$$\left[ \begin{array} { c c }
- \frac { 1 } { 5 } & - \frac { 1 } { 2 } \
- \frac { 1 } { 5 } & 0
\end{array} \right]$$

Question

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r } 
0 & - 5 \
- 2 & 2
\end{array} \right]$$
A)
$$\left[ \begin{array} { r r } 
- \frac { 1 } { 5 } & \frac { 1 } { 2 } \
\frac { 1 } { 5 } & 0
\end{array} \right]$$

B)
$$\left[ \begin{array} { c c } 
- \frac { 1 } { 5 } & 0 \
- \frac { 1 } { 5 } & - \frac { 1 } { 2 }
\end{array} \right]$$

C)

$$\left[ \begin{array} { r r } 
0 & - \frac { 1 } { 2 } \
- \frac { 1 } { 5 } & - \frac { 1 } { 5 }
\end{array} \right]$$

D)

$$\left[ \begin{array} { c c } 
- \frac { 1 } { 5 } & - \frac { 1 } { 2 } \
- \frac { 1 } { 5 } & 0
\end{array} \right]$$

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { r r } a & b \ c & d \end{array} \right]$ is $\frac{1}{ad-bc}\left[ \begin{array} { r r } d & -b \ -c & a \end{array} \right]$ if $ad-bc \neq 0$. For the given matrix, $ad-bc = 0(2) - (-5)(-2) = -10$. The inverse is $\frac{1}{-10}\left[ \begin{array} { r r } 2 & 5 \ 2 & 0 \end{array} \right] = \left[ \begin{array} { c c } -\frac{1}{5} & -\frac{1}{2} \ -\frac{1}{5} & 0 \end{array} \right]$.

Find the Inverse, If It Exists, for the Matrix [0−5−22]\left[ \begin{array} { r r } 0 & - 5 \\- 2 & 2\end{array} \right][0−2​−52​]

Find the Inverse, If It Exists, for the Matrix $\left[ \begin{array} { r r } 0 & - 5 \\- 2 & 2\end{array} \right]$