If A = [aij] is a scalar matrix of order n × n such that aii = k, for all i, then trace of A is equal to


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

(a) $n k$

(b) $n+k$

(c) $\frac{n}{k}$

(d) none of these


(a) $n k$


$A=\left[a_{i j}\right]_{n \times n}$

Trace of $A$, i. e. $\operatorname{tr}(A)=\sum_{i=1}^{n} a_{i j}=a_{11}+a_{22}+\ldots+a_{n n}$

$=k+k+k+\ldots n$ times

$=k n$

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