Question

If $A=\left[\begin{array}{cc}4& -2\\ 6& -3\end{array}\right]$, then $A^2$ is

• A. $\left[\begin{array}{cc}16& 4\\ 36& 9\end{array}\right]$
• B. $\left[\begin{array}{cc}8& -4\\ 12& -6\end{array}\right]$
• C. $\left[\begin{array}{cc}-4& 2\\ -6& 3\end{array}\right]$
• D. $\left[\begin{array}{cc}4& -2\\ 6& -3\end{array}\right]$

Answer 1

The correct option is D $\left[\begin{array}{cc}4& -2\\ 6& -3\end{array}\right]$

$A=\left[\begin{array}{cc}4& -2\\ 6& -3\end{array}\right]$

$A^2=\left[\begin{array}{cc}4& -2\\ 6& -3\end{array}\right]\times \left[\begin{array}{cc}4& -2\\ 6& -3\end{array}\right]$

using the multiplication properties of matrices, we get

$A^2=\left[\begin{array}{cc}4\times 4+(-2)\times 6& 4\times (-2)+(-2)\times (-3)\\ 6\times 4+(-3)\times 6& 6\times (-2)+(-3)\times (-3)\end{array}\right]$

$A^2=\left[\begin{array}{cc}4& -2\\ 6& -3\end{array}\right]$