📘 Question
Let \(A\) and \(B\) be matrices of orders \(3 \times 2\) and \(2 \times 4\) respectively. Find the order of matrix \(AB\).
✏️ Step-by-Step Solution
Step 1: Check multiplication condition
Matrix multiplication is possible if the number of columns of \(A\) equals the number of rows of \(B\).
\[
A_{3 \times 2}, \quad B_{2 \times 4}
\]
Since inner dimensions match (2 = 2), multiplication is possible.
Step 2: Determine resulting order
If:
\[
A_{m \times n} \cdot B_{n \times p} = AB_{m \times p}
\]
So,
\[
AB = 3 \times 4
\]
✅ Final Answer
\[
\boxed{3 \times 4}
\]
💡 Key Concept
In matrix multiplication:
- Inner dimensions must match
- Resulting matrix takes outer dimensions
So, \( (m \times n)(n \times p) = (m \times p) \)