Use MATLAB to define the following matrices:

\[\begin{array}{ll}\boldsymbol{A}=\begin{array}{cc}2 & 1 \\0 & 5 \\7 & 4\end{array} & \boldsymbol{B}=\begin{array}{cc}5 & 3 \\-2 & -4\end{array} \\\begin{array}{rrr}2 & 3 \\-5 & -2 \\0 & 3\end{array} & \boldsymbol{D}=\left[\begin{array}{ll}1 & 2\end{array}\right]\end{array}\]

Compute matrices and determinants if they exist.

(a) $\left(\mathbf{A C}^{\mathbf{T}}\right)^{-1}$

(b) $|\mathbf{B}|$

(c) $\left|\mathbf{A C}^{\mathbf{T}}\right|$

(d) $\left(\mathbf{C}^{\mathbf{T}} \mathbf{A}\right)^{-\mathbf{1}}$