Question

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

• A. $40$
• B. $45$
• C. $39$
• D. $5$

Answer 1

Answer: (A)

$40$

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

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

$=\left[\begin{array}{ccc}1& 6+12& 15\\ 4& 15+24& 30\\ 7& 3& 0\end{array}\right]$

Trace$=1+15+24$

$=40$

Option A is correct