Let the matrix \(A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}\) and \(AB = \begin{bmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{bmatrix}\) then order of B is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3 × 3
The product rule for orders: if A is of order m × n and B is of order n × p, then AB is defined and is of order m × p.
\(A \text{ is } 2 \times 3, \text{ so B must have 3 rows}\)
\(AB \text{ is } 2 \times 3, \text{ so B must have 3 columns}\)
Hence B is of order 3 × 3.