Question

Let $B$ be a matrix of order $3 \times 2$ and $C$ be a matrix of order $3 \times 3$. If $A$ is a matrix such that $BA = C$, then the order of $A$ is

• A. $2 \times 2$
• B. $2 \times 3$
• C. $3 \times 2$
• D. $3 \times 4$
• E. $3 \times 3$

Hint:

$(m \times n) \times (n \times p) \to (m \times p)$.

Answer 1

The Correct Option is B

Step 1: Concept
For matrix multiplication $B_{m \times n} A_{n \times p} = C_{m \times p}$.

Step 2: Analysis
Order of $B = 3 \times 2$. Order of $C = 3 \times 3$. Let order of $A = n \times p$.

Step 3: Conclusion
Number of columns of $B$ must equal number of rows of $A \implies n = 2$. Number of columns of $A$ must equal number of columns of $C \implies p = 3$. Order of $A = 2 \times 3$. Final Answer: (B)