Find the inverse of the matrix $\left[ \begin{array} { c c } 4 & - 5 \ 1 & 5 \end{array} \right]$ (if it exists).
A) $- \frac { 1 } { 25 } \left[ \begin{array} { c c } 5 & 5 \ - 1 & 4 \end{array} \right]$
B) $\frac { 1 } { 25 } \left[ \begin{array} { c c } 5 & 5 \ - 1 & 4 \end{array} \right]$
C) $\frac { 1 } { 25 } \left[ \begin{array} { c c } - 5 & - 5 \ 1 & - 4 \end{array} \right]$
D) $\frac { 1 } { 25 } \left[ \begin{array} { c c } 4 & - 5 \ 1 & 5 \end{array} \right]$
E) does not exist

Question

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is given by $\frac{1}{ad-bc} \left[ \begin{array} { c c } d & -b \ -c & a \end{array} \right]$. For the given matrix, $ad-bc = 4*5 - (-5)*1 = 25$, so its inverse is $\frac{1}{25} \left[ \begin{array} { c c } 5 & 5 \ -1 & 4 \end{array} \right]$.

Find the Inverse of the Matrix [4−515]\left[ \begin{array} { c c } 4 & - 5 \\ 1 & 5 \end{array} \right][41​−55​]

Find the Inverse of the Matrix $\left[ \begin{array} { c c } 4 & - 5 \\ 1 & 5 \end{array} \right]$