📘 Question
The number of all possible matrices of order \(3 \times 3\) with each entry 0 or 1 is:
(a) 27
(b) 18
(c) 81
(d) 512
✏️ Step-by-Step Solution
Step 1: Total entries
A \(3 \times 3\) matrix has:
\[
3 \times 3 = 9 \text{ entries}
\]
Step 2: Choices per entry
Each entry can be:
\[
0 \text{ or } 1 \Rightarrow 2 \text{ choices}
\]
Step 3: Total matrices
\[
\text{Total} = 2^9 = 512
\]
✅ Final Answer
\[
\boxed{(d)\; 512}
\]
💡 Key Concept
If a matrix has \(m \times n\) entries and each entry has \(k\) choices:
\[
\text{Total matrices} = k^{mn}
\]