Both eye dominance?

[odyssey1]

Is there such a thing?  

I've always been taught to shoot with both eyes open.  I've always noticed that while shooting weak hand, my left eye quickly picks up the sights.  When shooting right handed, my right eye picks up the sights.  My brother tried it, who is right eye dominant and right handed, could not pick up the sights with his left eye and had to cant the pistol a bit when shooting weak hand in order for his right eye to pick up the sight.

I've been shooting for over 30 years and had never learned to concept of eye dominance until I started surfing the web.  When checking for eye dominance, I'm right eye dominant.

Anyone else shoot this way?  Is this advantageous or detrimental?  I've been meaning to post this question but always forget to.

Thanks in advance for your replies.

[Hazcat]

I can shoot (badly ) with either hand rifle or pistol.  Never had a problem (other than trying to shoot right eye/ left hand and left eye / right hand).

[jnevis]

My problem is according to all the tricks to determine dominance I'm right eye dominant but when I shoot (both eyes open) I'm looking down the left side of the gun and hit wide unless I cant the gun towards the left or put my chin in my arm (putting the sights behind the left side).