The teacher hasn't uploaded a solution for this question yet.
Let the scalar matrix be represented as:
\[ \begin{bmatrix} k & 0 & 0 \\ 0 & k & 0 \\ 0 & 0 & k \end{bmatrix} \]The sum of all elements is given as 9:
\[k + 0 + 0 + 0 + k + 0 + 0 + 0 + k = 9\] \[3k = 9\] \[k = 3\]So, the scalar matrix is:
\[ \begin{bmatrix} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{bmatrix} \]The product of all elements is:
\[3 \times 0 \times 0 \times 0 \times 3 \times 0 \times 0 \times 0 \times 3 = 0\]Correct Answer: 0
AI generated content. Review strictly for academic accuracy.