Question

If $A = [a_{ij}]_{m \times n}$ be a scalar matrix, then trace of $A$ is equal to

• A. n
• B. 0
• C. $na_{11}$
• D. none of these

Answer 1

Answer: (C)

$na_{11}$

Answer 2

Trace of A is equal to the sum of diagonal elements of A $= a_{11} + a_{22}+a_{33} + .... +a_{nn}$ $= na_{11}$ ($\because$ all the diagonal elements of a scalar matrix are equal, $\therefore a_{11} = a_{22} = a_{33} = ... = a_{nn}$)