Chapter 3.3, Problem 46E

To determine

(a)

To find:

$\left|A^T\right|$ by using the matrix $A=\left[\begin{array}{ccc}1& 5& 4\\ 0& -6& 2\\ 0& 0& -3\end{array}\right]$.

To determine

(b)

To find:

$\left|A^2\right|$ by using the matrix $A=\left[\begin{array}{ccc}1& 5& 4\\ 0& -6& 2\\ 0& 0& -3\end{array}\right]$

To determine

(C)

To find:

$\left|A{A}^T\right|$ by using $A=\left[\begin{array}{ccc}1& 5& 4\\ 0& -6& 2\\ 0& 0& -3\end{array}\right]$

To determine

$(d)$

To find:

$\left|2A\right|$ by using the matrix $A=\left[\begin{array}{ccc}1& 5& 4\\ 0& -6& 2\\ 0& 0& -3\end{array}\right]$.

To determine

$(e)$

To find:

$\left|A^{-1}\right|$ by using $A=\left[\begin{array}{ccc}1& 5& 4\\ 0& -6& 2\\ 0& 0& -3\end{array}\right]$