Answer
Since A$A^{T}$ = I, the matrix is orthogonal.
$A^{-1}$= $\begin{bmatrix}
-4/5 & 3/5 \\
3/5 & 4/5
\end{bmatrix}$
Work Step by Step
If a matrix is orthogonal, then A$A^{T}$ = I. If a matrix is orthogonal, then the inverse of the matrix is equal to $A^{T}$.
First, we determine if A$A^{T}$ = I.
A = $\begin{bmatrix}
-4/5 & 3/5 \\
3/5 & 4/5
\end{bmatrix}$ $A^{T}$ = $\begin{bmatrix}
-4/5 & 3/5 \\
3/5 & 4/5
\end{bmatrix}$
A$A^{T}$ = $\begin{bmatrix}
.64 + .36 & (-.48) +.48 \\
(-.48) +.48 & .36 + .64
\end{bmatrix}$ = $\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}$
Since A$A^{T}$ = I, the matrix is orthogonal.
Since the matrix is orthogonal. $A^{-1}$ = $A^{T}$, so
$A^{-1}$= $\begin{bmatrix}
-4/5 & 3/5 \\
3/5 & 4/5
\end{bmatrix}$
