Answer:
B. [tex]\left[\begin{array}{cc}\frac{9}{61} &\frac{2}{61} \\\frac{10}{61} &\frac{9}{61} \end{array}\right][/tex]
Step-by-step explanation:
The given matrix is
[tex]\left[\begin{array}{cc}9&-2\\-10&9\end{array}\right][/tex]
The determinant of this matrix is
[tex]=9\times9--10\times-2=61[/tex]
Since the determinant is not zero, it means the inverse exists.
The inverse is given by
[tex]\frac{1}{determinant}\left[\begin{array}{cc}9&--2\\--10&9\end{array}\right][/tex]
[tex]\frac{1}{61}\left[\begin{array}{cc}9&2\\10&9\end{array}\right][/tex]
[tex]\left[\begin{array}{cc}\frac{9}{61} &\frac{2}{61} \\\frac{10}{61} &\frac{9}{61} \end{array}\right][/tex]
The correct choice is B.
