In Leftwrite, every inhabitant is either a lefty or a righty. Lefties write true statements with their left hand and false statements with their right hand. Righties write false statements with their left hand and true statements with their right hand.

• A and B are two inhibitants of Leftwrite who respectively wrote 3 statements, and 2 statements.
• Inhabitant A used the same hand to write all the 3 statements.
• Inhabitant B used different hands to write the 2 statements.

Here are the statements made by them:

Inhabitant A

1. I am a lefty writing with my left hand.
2. B is a righty.
3. B wrote statement-2 with his left hand.

Inhabitant B

1. A is a righty writing all the 3 statements with his left hand.
2. Each of A and myself is a righty.

What types do each of the 2 inhabitants belong to, and which hand/hands did they use to write their statements?