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

To find the inverse of a matrix, we use the formula:
$$	extbf{A}^{-1} = \frac{1}{	ext{det}(	extbf{A})} \left[ \begin{array} { c c } d & -b \ -c & a \end{array} ight]$$
where $	extbf{A} = \left[ \begin{array} { c c } a & b \ c & d \end{array} ight]$ and $	ext{det}(	extbf{A}) = ad - bc$.
Using this formula, we have:
$ 	ext{det}(	extbf{A}) = (4)(5) - (-5)(1) = 25$
$$	extbf{A}^{-1} = \frac{1}{25} \left[ \begin{array} { c c } 5 & 5 \ -1 & 4 \end{array} ight]$$
Therefore, the answer is (B).

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 $\left[ \begin{array} { c c } 4 & - 5 \\ 1 & 5 \end{array} \right]$