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Question
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
Options
nk
n + k
\[\frac{n}{k}\]
none of these
Solution
nk
\[Here, \]
\[A = \left[ a_{ij} \right]_{n \times n} \]
\[\text{Trace of} A, i . e . tr\left( A \right) = \sum a_{ij}^n{i = 1} = a_{11} + a_{22} + . . . + a_{nn} \]
\[ = k + k + k + . . .\text{ n times}\]
\[ = kn\]
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