Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}2 & 1 \\ 1 & 1\end{array}\right]$
- A$A^{-1}=\left[\begin{array}{cc}1 & -1 \\ -1 & 2\end{array}\right]$
- B$A^{-1}=\left[\begin{array}{cc}1 & 1 \\ 1 & 2\end{array}\right]$
- C$A^{-1}=\left[\begin{array}{cc}2 & -1 \\ -1 & 1\end{array}\right]$
- D$A^{-1}=\left[\begin{array}{cc}1 & -1 \\ 1 & 2\end{array}\right]$
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If $a$ is the determinant of the adjoint of the matrix $A = \begin{bmatrix} 1 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 3 \end{bmatrix}$ and $b$ is the determinant of the inverse of the matrix $B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & -3 & -1 \\ 2 & 1 & -4 \end{bmatrix}$,then find the value of $\frac{b+1}{18b}$.
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