Which state is known as "The Peace Garden State"?

Which state is known as "The Great Lakes State"? Which state is known as "The Mountain State"? Which state is known as "The Land of Enchantment"? Which state is known as "The Mount Rushmore State"? Which state's residents are called "Hoosiers"? Which state's residents are called "Buckeyes"? Which state's residents are called "Sooners"? Which state is the largest by area?