Let R be a ring with unity. Assume b1a=1R and ab2=1R. Prove that b1=b2.   Also, let R be a ring with unity. Assume a and b are both units. Prove that (ab)-1=b-1a-1.

Prove: Let R be a ring with identity, and let x ∈ R. Then the equation (-1)x = -x is true in R.

Let R be a ring. Let p = ax + b and q=cx² + dx + e be elements of R[x], for a, b, c, d, e E R. True or false: p and q may be equal as elements of R[x]. Select one: O True O False

Give an example of ring elements a and b with the proerties that ab = 0 but ba does not equal 0.