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
Yes.
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