Question

If A =$\left[\begin{array}{cc}a& b\\ b& a\end{array}\right]$ and $A^2$ =$\left[\begin{array}{cc}x& y\\ y& x\end{array}\right]$ , then

• A. x = a² + b² , y = 2ab
• B. x = 2ab, y = a + b
• C. x = a² – b² ,y = ab
• D. x = 2ab, y = a – b

Answer 1

The correct option is A

x = a² + b² , y = 2ab

$A=\left[\begin{array}{cc}a& b\\ b& a\end{array}\right]$
$A^2=\left[\begin{array}{cc}a& b\\ b& a\end{array}\right]\left[\begin{array}{cc}a& b\\ b& a\end{array}\right]=\left[\begin{array}{cc}{a}^2+b^2& ab+ab\\ ab+ab& b^2+a^2\end{array}\right]=\left[\begin{array}{cc}x& y\\ y& x\end{array}\right]$

Therefore $x=a^2+b^2$ and y = 2ab