Given the matrices $A = \left( \begin{array} { c c c } 2 & 1 & 0 \\ - 1 & 0 & 2 \end{array} \right)$ and $B = \left( \begin{array} { l l } b & 0 \\ 1 & b \end{array} \right)$, find:\ a) ( 0.5 points) Calculate the determinant of $A ^ { t } A$.\ b) ( 0.5 points) Calculate the rank of $B A$ as a function of $b$.\ c) (0.75 points) Calculate $B ^ { - 1 }$ for $b = 2$.\ d) ( 0.75 points) For $b = 1$, calculate $B ^ { 5 }$.