Question

Find the inverse of the matrix, if it exists (Picture provided)

Answer 1

Answer:

B. $\left[\begin{array}{cc}\frac{9}{61} &\frac{2}{61} \\\frac{10}{61} &\frac{9}{61} \end{array}\right]$

Step-by-step explanation:

The given matrix is

$\left[\begin{array}{cc}9&-2\\-10&9\end{array}\right]$

The determinant of this matrix is

$=9\times9--10\times-2=61$

Since the determinant is not zero, it means the inverse exists.

The inverse is given by

$\frac{1}{determinant}\left[\begin{array}{cc}9&--2\\--10&9\end{array}\right]$

$\frac{1}{61}\left[\begin{array}{cc}9&2\\10&9\end{array}\right]$

$\left[\begin{array}{cc}\frac{9}{61} &\frac{2}{61} \\\frac{10}{61} &\frac{9}{61} \end{array}\right]$

The correct choice is B.