Question

If \( A = [a_{ij}]_{m \times n} \) and \( B = [b_{ij}]_{j \times p} \), then order of \( AB \) will be \( m \times p \).

Hint:

The order of the product of two matrices is determined by the outer dimensions, i.e., the rows of the first matrix and the columns of the second.

Answer 1

Step 1: Matrix multiplication rule.
The product of two matrices \( A \) and \( B \) can only be formed if the number of columns of \( A \) is equal to the number of rows of \( B \). The order of the resulting matrix \( AB \) will be \( m \times p \), where \( A \) is of order \( m \times n \) and \( B \) is of order \( n \times p \).

Step 2: Conclusion.
Thus, the order of \( AB \) is \( m \times p \), which makes the statement true.