Question

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

Hint:

The inner dimensions must match in matrix multiplication: $(a \times b)(b \times c) = a \times c$.

Answer 1

The Correct Option is A

Step 1: Understand matrix multiplication rules.
A $3 \times 2$ matrix multiplied by an $m \times n$ matrix results in a $3 \times n$ matrix.
Step 2: Compare with the result matrix.
The resulting matrix is $3 \times 3$. So the second matrix must have 3 columns (n = 3). Since the first matrix is $3 \times 2$, R must be $2 \times 3$ for multiplication to be valid.
Step 3: Conclusion.
Thus, R is a $2 \times 3$ matrix.