1. **Problem statement:** Find the inverse of matrix $$A = \begin{bmatrix} 2 & 7 \\ 3 & 11 \end{bmatrix}$$. 2. **Formula for inverse of a 2x2 matrix:** For $$A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$$, the inverse is given by $$A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$$, provided that the determinant $$ad - bc \neq 0$$. 3. **Calculate the determinant:** $$\det(A) = (2)(11) - (7)(3) = 22 - 21 = 1$$. Since the determinant is 1, the inverse exists. 4. **Apply the formula:** $$A^{-1} = \frac{1}{1} \begin{bmatrix} 11 & -7 \\ -3 & 2 \end{bmatrix} = \begin{bmatrix} 11 & -7 \\ -3 & 2 \end{bmatrix}$$. 5. **Conclusion:** The inverse matrix is $$\begin{bmatrix} 11 & -7 \\ -3 & 2 \end{bmatrix}$$, which corresponds to option (B).