Question

If $A=\left[\begin{array}{cc}1& 3\\ 8& 9\end{array}\right]$, find the sum of the principal diagonal elements of $A^2-A.2$

• A. 120
• B. 63
• C. 85
• D. 53

Answer 1

The correct option is A

120

$A=\left[\begin{array}{cc}1& 3\\ 8& 9\end{array}\right]A^2=\left[\begin{array}{cc}1& 3\\ 8& 9\end{array}\right]\left[\begin{array}{cc}1& 3\\ 8& 9\end{array}\right]=\left[\begin{array}{cc}25& 30\\ 80& 105\end{array}\right]A^2-A=\left[\begin{array}{cc}24& 27\\ 72& 96\end{array}\right]$
Sum of the principal diagonal elements is 120