- #1
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- 11
Okay, so if r,s are elements of R and rs = 0 then either r or s has to equal zero.
I'm just confused because it seems that if rs = 0 then we can show that both r and s must be zero.... I don't know what i'm doing wrong..
rs = 0
r^-1(rs) = r^-1(0) = 0
1s = 0
s = 0
and then:
rs = 0
r(ss^-1) = (0)s^-1 = 0
r1 = 0 = 0
r = 0
I mean, both r and s have multiplicative inverses so it seems like r and s both need to be zero by this logic.. what am i doing wrong here?
I'm just confused because it seems that if rs = 0 then we can show that both r and s must be zero.... I don't know what i'm doing wrong..
rs = 0
r^-1(rs) = r^-1(0) = 0
1s = 0
s = 0
and then:
rs = 0
r(ss^-1) = (0)s^-1 = 0
r1 = 0 = 0
r = 0
I mean, both r and s have multiplicative inverses so it seems like r and s both need to be zero by this logic.. what am i doing wrong here?