Question

If $A=\left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]$ and $I$ is the unit matrix of order 2, then $A^2$ is equal to

• A. $4A-3I$
• B. $3A-4I$
• C. $A-I$
• D. $A+I$

Answer 1

Answer: (A)

$A^2=AA=\left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]\left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]$
$=\left[\begin{array}{cc}5& -4\\ -4& 5\end{array}\right]=\left[\begin{array}{cc}8& -4\\ -4& 8\end{array}\right]-\left[\begin{array}{cc}3& 0\\ 0& 3\end{array}\right]$
$=4A-3I$