Question

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

Options

• nk

• n + k 

• \[\frac{n}{k}\] 

• none of these

   

Answer 1

 nk 

\[Here, \]

\[A = \left[ a_{ij} \right]_{n \times n} \]

\[\text{Trace of} A, i . e . tr\left( A \right) = \sum a_{ij}^n{i = 1} = a_{11} + a_{22} + . . . + a_{nn} \]

\[ = k + k + k + . . .\text{ n times}\]

\[ = kn\]