If A2 = I, where I is the identity matrix, which matrix correctly represents matrix A?

We know that [tex] \boldsymbol{A^2}=\boldsymbol{A\times A} [/tex]We also know that [tex] \boldsymbol{I}=\begin{bmatrix}
1 &0 \\
0&1
\end{bmatrix} [/tex]Now, it has been given to us that [tex] \boldsymbol{A^2}=\boldsymbol{I} [/tex]Therefore, we will have to find the correct [tex] \boldsymbol{A} [/tex] from the given options and we find that when:[tex] \boldsymbol{A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix} [/tex]then [tex] \boldsymbol{A^2}=\boldsymbol{A\times A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}\times \begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}=\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix} [/tex]Therefore, from the above given options, Option C is the correct option.Therefore, [tex] \boldsymbol{A}=\begin{bmatrix}
3 & -2\\
4 & -3
\end{bmatrix} [/tex] is the correct answer.