If the sum of all elements of a \( 3\times 3 \) scalar matrix is 9, then the product of all its elements is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
A scalar matrix of order 3 is \( k\mathrm{I} \): k on the diagonal and 0 everywhere else.
The sum of its elements is
\( \displaystyle 3k=9\ \Rightarrow\ k=3 \)
Six of the nine elements are 0, so the product of all the elements is 0.