Given the matrices $A = \left(\begin{array}{ccc} 0 & -1 & 2 \\ 2 & 1 & -1 \\ 1 & 0 & 1 \end{array}\right)$, $I = \left(\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right)$, $B = \left(\begin{array}{cc} 2 & -1 \\ 1 & 0 \\ 0 & 1 \end{array}\right)$, find:\ a) (1 point) Calculate, if possible, the inverse of matrix $A$.\ b) (0.5 points) Calculate the matrix $C = A^{2} - 2I$.\ c) (1 point) Calculate the determinant of matrix $D = ABB^{t}$ (where $B^{t}$ denotes the transpose of matrix $B$).