Find the Order of Matrix B
Given:
\[ A \text{ is of order } 2 \times 3 \]
Step 1: Find AT
\[ A^T \text{ is of order } 3 \times 2 \]
Step 2: Condition for ATB
\[ A^T (3 \times 2) \cdot B \Rightarrow \text{columns of } A^T = \text{rows of } B \]
\[ 2 = \text{rows of } B \]
Step 3: Condition for BAT
\[ B \cdot A^T (3 \times 2) \Rightarrow \text{columns of } B = \text{rows of } A^T \]
\[ \text{columns of } B = 3 \]
Final Answer:
\[ \boxed{B \text{ is of order } 2 \times 3} \]