📘 Question
The number of possible matrices of order \(3 \times 3\) with each entry 0 or 2 is:
(a) 9
(b) 27
(c) 81
(d) none of these
✏️ Step-by-Step Solution
Step 1: Total entries
\[
3 \times 3 = 9 \text{ entries}
\]
Step 2: Choices per entry
Each entry can be:
\[
0 \text{ or } 2 \Rightarrow 2 \text{ choices}
\]
Step 3: Total matrices
\[
\text{Total} = 2^9 = 512
\]
Step 4: Match options
512 is not given in options.
✅ Final Answer
\[
\boxed{(d)\; \text{none of these}}
\]
💡 Key Concept
If each entry has \(k\) choices and total entries are \(mn\), then:
\[
\text{Total matrices} = k^{mn}
\]