Given the matrix \( A = \begin{bmatrix} 3 & 4 \\ 2 & 3 \end{bmatrix} \), find the matrix \( B \) such that \( AB = I \), where \( I \) is the identity matrix.

Step 1 ：To find the matrix \( B \), we need to solve the equation \( AB = I \).

Step 2 ：The identity matrix \( I \) is \( \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \).

Step 3 ：Let \( B = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \). Then, \( AB = \begin{bmatrix} 3a+4c & 3b+4d \\ 2a+3c & 2b+3d \end{bmatrix} \).

Step 4 ：Setting this equal to the identity matrix gives us the system of equations \( \begin{cases} 3a+4c = 1 \\ 3b+4d = 0 \\ 2a+3c = 0 \\ 2b+3d = 1 \end{cases} \).

Step 5 ：Solving this system of equations gives \( a = 1/3 \\ b = -1/2 \\ c = -1/6 \\ d = 2/3 \).

Step 6 ：Therefore, \( B = \begin{bmatrix} 1/3 & -1/2 \\ -1/6 & 2/3 \end{bmatrix} \).