Question

If $A=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 1& 0\end{array}\right],B=\left[\begin{array}{ccc}1& 0& 0\\ 0& 3& 0\\ 0& 4& 5\end{array}\right],\mathrm{Trace}\left(BA\right)$ is equal to

• A. 40
• B. 45
• C. 39
• D. 5

Answer 1

The correct option is A 40

Given $B=\left[\begin{array}{ccc}1& 0& 0\\ 0& 3& 0\\ 0& 4& 5\end{array}\right],A=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 1& 0\end{array}\right]$

$BA=\left[\begin{array}{ccc}1& 0& 0\\ 0& 3& 0\\ 0& 4& 5\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 1& 0\end{array}\right]$

$BA=\left[\begin{array}{ccc}1& 2& 3\\ 12& 15& 18\\ 51& 25& 24\end{array}\right]$

Trace of $BA$ is sum of diagonal elements of matrix $BA$

$1+15+24=40$

$Trace\left(BA\right)=40$