00:01
Okay, so for the statement, we want to show that if a divides b and b divides a, then a is equal to b or a is equal to negative b.
00:09
So to show this, if we have a divides by b, this implies there exists an integer c or in integers such that a c is equal to b.
00:22
And opposite, when a, sorry, when b divides a, this implies that there exists an integer d, in integers such that b, d is equal to a.
00:34
So what we'll do is we'll substitute, sorry, sorry, we will substitute b into here.
00:41
So we have ac times by d is equal to a and expanding we have a, c, d is equal to a.
00:50
But you'll notice that these two a's are equal, so they're the same letter.
00:56
So that means by the identity property of multiplication, cd must be equal to one.
01:02
So this implies that cd is equal to 1...