It does matter in which county you are.
What I know is; Some places in Belgium they do.
In the US Military, you are authorized to salute with your left hand when:
You are a band major
You are opening the door for a dignitary, with your right hand (i.e the U.S. President)
Your right hand/arm is injured
Rifle salute, it is a salute done while performing rifle manual movements
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