[tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
We can find the A as shown below:
Given A^2=I
We know that A^2=A×A
And [tex]I=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
So, [tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Let [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right] \left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}9-8&-6+6\\12-12&-8+9\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Hence, [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
Hence, option C is correct
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