Question

lf $A=\left[a_{ij}\right]$ is a scalar matrix of order $n\times n$ such that $a_{ij}=k$ for all $i=j$, then trace of $A=$

• A. $nk$
• B. $n+k$
• C. $\frac{n}{k}$
• D. $1$

Answer 1

The correct option is A $nk$

$\left[\begin{array}{ccc}k& 0& ...0\\ .& k& \\ ..0& 0& k\end{array}\right](m\times n)$
$\therefore$ m columns and n rows
$={\sum }_{i=1}^{n}aij(wherei=j)$
$={\sum }_{i=1}^{n}k$
$=nk$ ( $\because k=aij(ifi=j)$)