If (a] € Z/mZ is invertible, is [-a] invertible? If yes, prove it and say what the multiplicative inverse of [-a][-a] is. If no, give a counterexample (including m and a).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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If [a] € Z/mZ is invertible, is [-a] invertible?
If yes, prove it and say what the multiplicative inverse of [-a][-a] is.
If no, give a counterexample (including m and a).
Sappise
Caj? = [b]
ab - LIJM =It km
wts
[-aJ" = [-b]
-a: n-a
-b- n-b
(m-a) (m -b)
Em- Carb) mt ab
-(m-a b)u tab
- (m-a -btk)mt)
Yes, is t-a) inveritble.
Transcribed Image Text:If [a] € Z/mZ is invertible, is [-a] invertible? If yes, prove it and say what the multiplicative inverse of [-a][-a] is. If no, give a counterexample (including m and a). Sappise Caj? = [b] ab - LIJM =It km wts [-aJ" = [-b] -a: n-a -b- n-b (m-a) (m -b) Em- Carb) mt ab -(m-a b)u tab - (m-a -btk)mt) Yes, is t-a) inveritble.
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