Chapter 3.3, Problem 44E

To determine

(a)

To find:

$\left|A^T\right|$ by using the matrix $A=\left[\begin{array}{cc}-4& 10\\ 5& 6\end{array}\right]$.

To determine

(b)

To find:

$\left|A^2\right|$ by using the matrix $A=\left[\begin{array}{cc}-4& 10\\ 5& 6\end{array}\right]$.

To determine

(C)

To find:

$\left|A{A}^T\right|$ by using $A=\left[\begin{array}{cc}-4& 10\\ 5& 6\end{array}\right]$

To determine

$(d)$

To find:

$\left|2A\right|$ by using the matrix $A=\left[\begin{array}{cc}-4& 10\\ 5& 6\end{array}\right]$.

To determine

$(e)$

To find:

$\left|A^{-1}\right|$ by using the matrix $A=\left[\begin{array}{cc}-4& 10\\ 5& 6\end{array}\right]$