Questionthe inverse of $$A=\left(\begin{array}{cc} 3 & -5 \\ -2 & 3 \end{array}\right)$$

Studdy Solution
Apply the formula for the inverse of a 2x2 matrix. The inverse $A^{-1}$ is given by:
$$A^{-1} = \frac{1}{\det(A)} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$$
Substitute the values from matrix $A$:
$$A^{-1} = \frac{1}{-1} \begin{pmatrix} 3 & 5 \\ 2 & 3 \end{pmatrix}$$
$$A^{-1} = \begin{pmatrix} -3 & -5 \\ -2 & -3 \end{pmatrix}$$
The inverse of matrix $A$ is:
$$A^{-1} = \begin{pmatrix} -3 & -5 \\ -2 & -3 \end{pmatrix}$$