About Matrix Inverse

The inverse of a 2x2 matrix \( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) is:

• \( A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \), if \( ad - bc \neq 0 \).

Example: For \( A = \begin{bmatrix} 4 & 3 \\ 3 & 2 \end{bmatrix} \), \( \det(A) = 8 - 9 = -1 \), so \( A^{-1} = \frac{1}{-1} \begin{bmatrix} 2 & -3 \\ -3 & 4 \end{bmatrix} = \begin{bmatrix} -2 & 3 \\ 3 & -4 \end{bmatrix} \).