Find the inverse of the matrix $\left[ \begin{array} { c c } 8 & 16 \ - 24 & - 40 \end{array} \right]$.
A) $\frac { 1 } { 7 } \left[ \begin{array} { c c } 8 & 16 \ - 24 & - 40 \end{array} \right]$
B) $\frac { 1 } { 8 } \left[ \begin{array} { c c } - 5 & - 2 \ 3 & 1 \end{array} \right]$
C) $\left[ \begin{array} { c c } - 8 & - 16 \ 40 & 24 \end{array} \right]$
D) $\left[ \begin{array} { c c } 8 & - 24 \ 32 & - 56 \end{array} \right]$
E) $\frac { 1 } { 13 } \left[ \begin{array} { c c } - 8 & - 16 \ - 24 & 40 \end{array} \right]$

Question

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 the given matrix, $ad-bc = 8(-40) - 16(-24) = -320 + 384 = 64$, so the inverse is $\frac{1}{64}\left[ \begin{array} { c c } -40 & -16 \ 24 & 8 \end{array} \right] = \frac{1}{8}\left[ \begin{array} { c c } -5 & -2 \ 3 & 1 \end{array} \right]$.

Find the Inverse of the Matrix [816−24−40]\left[ \begin{array} { c c } 8 & 16 \\ - 24 & - 40 \end{array} \right][8−24​16−40​]

Find the Inverse of the Matrix $\left[ \begin{array} { c c } 8 & 16 \\ - 24 & - 40 \end{array} \right]$