Lecture 15 | Let G be a group then orders of the element of G and its inverse are same

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Proof: Group Element is the Inverse of its Inverse | Abstract Algebra Proof: Group Element is the Inverse of its Inverse | Abstract Algebra
If each element of a group G is its own inverse, then show that G is abelian. If each element of a group G is its own inverse, then show that G is abelian.
Show that in a group G, orders or element and its inverse are same. Show that in a group G, orders or element and its inverse are same.
let g be an element (non-identity) of a group G then g is its own inverse iff g is of order 2 let g be an element (non-identity) of a group G then g is its own inverse iff g is of order 2
let G be a group & x be an element of odd order in G then for any element y in G their exist y^2=x let G be a group & x be an element of odd order in G then for any element y in G their exist y^2=x
(Abstract Algebra 1) Definition of a Cyclic Group (Abstract Algebra 1) Definition of a Cyclic Group
12. If G is a group such that x.x=e for all x∈G then G is an abelian group 12. If G is a group such that x.x=e for all x∈G then G is an abelian group
show that if every element of the group G is its own inverse then G is abelian show that if every element of the group G is its own inverse then G is abelian