Question

Prove that if g E G has the property g*g=g, where * is the group
operation of G, then g is the identity element of G.​

Answer 1

Answer:

A group G is a set with a binary operation · which maps a pair (g,h) in GxG to g·h in G, which satisfies: The operation is associative, that is to say (f·g)·h=f·(g·h) for any three (not necessarily distinct) elements of G. There is an element e in G, called an identity element, such that g·e=g=e·g for every g in G.

Answer 2

Step-by-step explanation:

The length of a metal is ????₁ when the tension in it is T₁ and

is ????₂ when the tension is T₂. The original length of the wire

is

(a)????₁ + ????₂/2

(b)????₁T₂ + ????₂T₁/T₁ + T₂

(c)????₁T₂ + ????₂T₁/T₂ - T₁

(d) √T₁T₂????₁????₂