Question

If \( AB = C \) where \( B \) and \( C \) are of order \( 3 \times 5 \), then the order of \( A \) is:

Hint:

The order of a matrix product is determined by the rows of the first matrix and the columns of the second matrix. The result of \( AB \) will have the number of rows of \( A \) and the number of columns of \( B \).

Answer 1

Step 1: Using the property of matrix multiplication.
When multiplying two matrices, the number of columns of the first matrix must equal the number of rows of the second matrix.
Given that \( B \) is of order \( 3 \times 5 \) and \( C \) is of order \( 3 \times 5 \), matrix \( A \) must have \( 3 \) rows to match with the 3 rows of \( C \). Therefore, matrix \( A \) must have 3 rows and 3 columns, i.e., matrix \( A \) has an order of \( 3 \times 3 \).
Step 2: Conclusion.
Thus, the order of matrix \( A \) is \( 3 \times 3 \).