The number of all different possible matrices of order 2 × 2 with each entry −1, 0 or 1 is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 81
A 2 × 2 matrix has 4 entries, and each entry can be chosen in 3 ways (−1, 0 or 1), independently of the others.
By the multiplication principle:
\(\text{number of matrices} = 3 \times 3 \times 3 \times 3\)
\(= 3^4 = 81\)
Tip: With k possible values for each entry, the number of m × n matrices is \(k^{mn}\), not \((mn)^k\). Here \(3^4 = 81\), while \(4^3 = 64\) is the common slip.