Question

(a) If orders of matrices A and B are \( p \times q \) and \( q \times r \) respectively, then order of AB is:

• A. \( p \times r \)
• B. \( r \times p \)
• C. \( q \times p \)
• D. None of these

Hint:

In matrix multiplication, the number of columns in the first matrix must match the number of rows in the second matrix. The resulting matrix takes the row count from the first and column count from the second matrix.

Answer 1

The Correct Option is A

Understanding matrix multiplication order. If \( A \) is of order \( p \times q \) and \( B \) is of order \( q \times r \), then the resulting matrix \( AB \) has order: \[ (p \times q) \cdot (q \times r) = p \times r \]