Let \(A = [a_{ij}]\) be a square matrix of order 3 with each entry either 0 or 1, then the number of all such possible matrices is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 512
A square matrix of order 3 has 3 × 3 = 9 entries, and each entry can be chosen in 2 ways (0 or 1). By the multiplication principle:
\(2 \times 2 \times \cdots \times 2 \text{ (9 times)} = 2^9 = 512\)
Tip: The count is (choices per entry)(number of entries), here \(2^9\), not \(9^2 = 81\).
NCERT (2026-27 edition):
Types of Matrices
