📘 Question
If \(A\) and \(B\) are matrices of order \(3 \times m\) and \(3 \times n\) respectively and \(m = n\), find the order of:
\[
5A – 2B
\]
(a) \(m \times 3\)
(b) \(3 \times 3\)
(c) \(m \times n\)
(d) \(3 \times n\)
✏️ Step-by-Step Solution
Step 1: Orders of matrices
\[
A = 3 \times m,\quad B = 3 \times n
\]
Given:
\[
m = n
\]
So both matrices are:
\[
3 \times n
\]
—
Step 2: Condition for subtraction
Matrix subtraction is possible only when orders are equal.
Thus:
\[
5A – 2B \text{ has same order } = 3 \times n
\]
—
✅ Final Answer
\[
\boxed{(d)\; 3 \times n}
\]
—
💡 Key Concept
Scalar multiplication does not change matrix order. Addition/subtraction requires same dimensions and keeps the same order.