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Explain Solution R.D.Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 32 maths Textbook Solution.

Answers (1)

Answer: The correct option is (A).

Given:A=\left[a_{i j}\right]_{m \times n} \text { and } a_{i j}=K


\because A=\left[a_{\ddot{j}}\right]_{m \times n}

Trace of A, i.e,

\begin{aligned} \operatorname{tr}(A)=\sum a_{i j}^{n i}=1 &=a_{11}+a_{22}+a_{33}+\ldots .+a_{n n} \\ &=K+K+K+K \ldots . \quad \text { (n times) } \\ &=K(n) \\ &=n K \end{aligned}

Thus, the correct option is (A).

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