Question

If a2 = i, where i is the identity matrix, which matrix correctly represents matrix a?

Answer 1

$A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]$

We can find the A as shown below:

Given A^2=I

We know that A^2=A×A

And $I=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

So, $A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Let $A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]$

$A^2=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right] \left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]$

$A^2=\left[\begin{array}{ccc}9-8&-6+6\\12-12&-8+9\end{array}\right]$

$A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Hence, $A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]$

Hence, option C is correct

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