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Consider the rectangle in a multiplication table where the left side of the rectangle is in the column for p times table; the right side of the rectangle is in the column for q times table. Also suppose the top of the rectangle is in the row for the r times table and the bottom of the rectangle is in the row for the s times table.

Schematically,

----p------q

----|-------|

r---a-----b

----|------|

----|------|

s--c-----d

Suppose the numbers in the four corners of the rectangle are a, b, c and d.

Then

a = pr, b = qr, c = ps and d = qs

So the product of opposite corners are

ad = pr x qs = pqrs

bc = qr x ps = pqrs

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12y ago

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