Why is it that when you multiply each pair of numbers at opposite corners of any rectangle of a multiplication chart the products are equal?

In a multiplication chart, the value at each cell corresponds to the product of the numbers at the corresponding row and column headers. When you multiply the numbers at opposite corners of a rectangle, you're essentially calculating the products of the same two numbers but in different orders. This is due to the commutative property of multiplication, which states that (a \times b = b \times a). Therefore, the products remain equal regardless of the order in which the numbers are multiplied.