In The Name of Allaah, The Most Merciful, The Bestower of Mercy.
Questioner: I am left-handed; I have used my left hand since childhood and I grew up upon that. At present when I perform ablution, I use it (i.e. my left hand) to pour the water and the right hand to wash (the limbs); so I don’t know whether my ablution is correct or not. Likewise, I use my left hand when using the Siwaak and when writing; but I use my right hand when eating. However, besides the ablution (i.e. during which I use my left hand to pour the water), I am in doubt about using it (when doing other things).
Answer: There is no harm in this [i.e. in using your left hand] besides the Istinjaa [i.e. when using water to clean your private parts after using the toilet]. There is no harm if you were to use your right hand to wipe over your head, wash your face, forearms and feet whilst carrying the water with your left hand. However, when performing Istinjaa, it is the left hand that should touch the private parts and the right hand is used to pour the water for cleaning oneself; for indeed the Prophet [sallal-laahu-alayhi-wasallam] said, “Do not breathe in the drinking utensil”, meaning, when drinking; ”And he [i.e. the person] should not [touch or clean his private parts] with his right hand whilst in the khalaa (i.e. in the place of urination or defecation)]”. 
So Istinjaa is performed with the left hand and it is what is to touch [the private parts] and the right hand is used to pour the water. As for the other affairs [i.e. writing, siwaak], there is no harm [in using the left hand] In-Shaa-Allaah. [Source: Al-Fataawaa Wad-Duroos Fil Masjid Al-Haraam Pages 151-152. By Shaikh Abdullah Bin Muhammad Bin Humaid]
 Bukhaari Numbers 153 and 154 and Muslim number: 267]