I have absolutely no idea on how I go about doing algebraic proofs. Geometric proofs make sense but the algebra ones are like greek. How should I think about doing a albraic proof. For example, prove that x multiplied by -1 = -x:confused::confused::confused:

Here's a thought.

A ring with identity is a ring R that contains an element 1_{R} and satisfies the

axiom a\cdot 1_{R}=a=1_{R}a, \;\ \forall a \in R

This is called a multiplicative identity.

Therefore, (-1_{R})a=-(1_{R}a)=-(a)=-a