Find the inverse of the matrix [tex]\left[\begin{array}{ccc}9&-2\\-10&9\\\end{array}\right][/tex] , if it exist.

Answer:The answer is (b)Step-by-step explanation:* Lets check how to find the inverse of the matrix,  its dimensions is 2 × 2* To know if the inverse of the matrix exist find the determinant- If its not equal 0, then it exist* How to find the determinant- It is the difference between the multiplication of  the diagonals of the matrixEx: If the matrix is [tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]      its determinant = ad - bc- After that lets swap the positions of a and d, put negatives  in front of b and c, and divide everything by the determinant- The inverse will be [tex]\left[\begin{array}{ccc}\frac{d}{ad-bc} &\frac{-b}{ad-bc}\\\frac{-c}{ad-bc} &\frac{a}{ad-bc}\end{array}\right][/tex]* Lets do that with our problem∵ The determinant = (9 × 9) - (-2 × -10) = 81 - 20 = 61- The determinant ≠ 0, then the inverse is exist∴ The inverse is [tex]\frac{1}{61}\left[\begin{array}{ccc}9&2\\10&9\end{array}\right][/tex]=    [tex]\left[\begin{array}{ccc}\frac{9}{61}&\frac{2}{61}\\\frac{10}{61} &\frac{9}{61}\end{array}\right][/tex]* The answer is (b)