Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
-$$A = \left[ \begin{array} { l l }
- 3 & 4 \
- 5 & 3
\end{array} \right]$$
A) $A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & \frac { 4 } { 11 } \ - \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]$
B) $A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & - \frac { 4 } { 11 } \ \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]$
C) Singular matrix
D) $A ^ { - 1 } = \left[ \begin{array} { c c } - \frac { 3 } { 11 } & \frac { 4 } { 11 } \ - \frac { 5 } { 11 } & \frac { 3 } { 11 } \end{array} \right]$

Question

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
-$$A = \left[ \begin{array} { l l } 
- 3 & 4 \
- 5 & 3
\end{array} \right]$$
A) $A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & \frac { 4 } { 11 } \ - \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]$
B) $A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & - \frac { 4 } { 11 } \ \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]$
C) Singular matrix
D) $A ^ { - 1 } = \left[ \begin{array} { c c } - \frac { 3 } { 11 } & \frac { 4 } { 11 } \ - \frac { 5 } { 11 } & \frac { 3 } { 11 } \end{array} \right]$

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is $\frac{1}{ad-bc}\left[ \begin{array} { c c } d & -b \ -c & a \end{array} \right]$. For matrix A, $ad-bc = (-3)(3) - (4)(-5) = -9 + 20 = 11$, so the inverse is $\frac{1}{11}\left[ \begin{array} { c c } 3 & -4 \ 5 & -3 \end{array} \right]$, which matches choice B.

Determine the Inverse of the Given Matrix, If Possible A=[−34−53]A = \left[ \begin{array} { l l } - 3 & 4 \\- 5 & 3\end{array} \right]A=[−3−5​43​]

Determine the Inverse of the Given Matrix, If Possible $A = \left[ \begin{array} { l l } - 3 & 4 \\- 5 & 3\end{array} \right]$