Question

If $A=\left[\begin{array}{cc}1& 4\\ -1& 1\end{array}\right]$ Find $A^2$

Answer 1

$A^2=A.A=\left[\begin{array}{cc}1& 4\\ -1& 1\end{array}\right].\left[\begin{array}{cc}1& 4\\ -1& 1\end{array}\right]$

$=\left[\begin{array}{cc}1\times 1+4\times -1& 1\times 4+4\times 1\\ -1\times 1+1\times -1& -1\times 4+1\times 1\end{array}\right]$

$=\left[\begin{array}{cc}1-4& 4+4\\ -1-1& -4+1\end{array}\right]$

$=\left[\begin{array}{cc}-3& 8\\ -2& -3\end{array}\right]$