What's the opposite of origin?

if a = 0, then

a + b = b

b + a = b

a - b = -b

b - a = b

a * b = a

b * a = a

a ÷ b = a

b ÷ a = undefined

if c doesn't have value, will it be possible?

c + b = c

b + c = c

c - b = c

b - c = - c

c * b = b

b * c = b

c ÷ b = b

b ÷ c = undefined