In the Indian Armed Forces & British Army, if a Soldier’s right arm is incapacitated (In a sling or plaster cast for example) he does not salute with his left, he would merely brace his body up and greet the officer verbally.
In US Army, Saluting with the left is permitted when the right is incapacitated due to battle injury.
Example: A person with his right arm in a sling would be permitted to salute with the left. If a person has had his right arm amputated he would probably no longer be on active duty.
Veterans are allowed to render a salute and if as cited above may use the left arm to render honors.
Saluting with a metal hand(hook)
Saluting with a prosthetic arm.
When is it correct to salute with your left hand? ONLY if you are in US Air Force ABU’s wearing a Trident and a SF tab at a Clinton or Sanders rally. — In most cases around the world – If a Soldier has lost an arm he would receive a medical discharge.
This answer was written by Sonu Singh on Quora.