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Triangular Matrix

If A=[ai j] i...

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
(a) nk
(b) n + k
(c) $\frac{n}{k}$
(d) none of these

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Solution

(a) nk

$Here, A = {[a_{i j}]}_{n \times n} Trace of A, i . e . tr (A) = {\sum a_{i j}}_{i = 1}^{n} = a_{11} + a_{22} + . . . + a_{n n} = k + k + k + . . . n times = k n$

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