The image shows a $2 \times 2$ matrix $A$ and asks to find its inverse, $A^{-1}$.

The matrix $A$ is: $A = \begin{pmatrix} 9 & 7 \\ 3 & 5 \end{pmatrix}$

The formula for the inverse of a $2 \times 2$ matrix $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is: $A^{-1} = \frac{1}{ad - bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$

For your matrix:

• $a = 9$
• $b = 7$
• $c = 3$
• $d = 5$

Let me calculate the determinant and the inverse matrix.The determinant of matrix $A$ is $24$, which means the matrix is invertible.

The inverse of matrix $A$ is: $A^{-1} = \begin{pmatrix} 0.2083 & -0.2917 \\ -0.125 & 0.375 \end{pmatrix}$

Would you like more details on the steps, or do you have any other questions?

Here are five related questions you might find useful:

1. How can I verify if a matrix is invertible without calculating the determinant?
2. What is the geometric interpretation of a matrix inverse?
3. How are inverse matrices used in solving systems of equations?
4. What happens when a matrix is singular (non-invertible)?
5. Can every square matrix be inverted?

Tip: Always check if the determinant of a matrix is non-zero before calculating its inverse!