Question

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

Answer 1

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

$=\left[\begin{array}{cc}2\times 2+(-1\times -1)& 2\times -1+(-1\times 2)\\ -1\times 2+2\times -1& -1\times -1+2\times 2\end{array}\right]$

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

$=\left[\begin{array}{cc}5& -4\\ -4& 5\end{array}\right]$