Question

If $A=\left[a_{ij}\right]$ is a scalar matrix of order $n\times n$ such that $a_{ij}=k$ for all then trace of A is equal to

• A. $nk$
• B. $n+k$
• C. $n/k$
• D. none of these

Answer 1

The correct option is A $nk$

By definition of trace of a scalar matrix of order n,
$tr\left(A\right)=a_{11}+a_{22}+a_{33}+.....+a_{nn}$
$=k+k+....k$ (upto n times)
$tr\left(A\right)=nk$