Answer:
Consider,
F = (m, n) be the inverse in A ∀ m ∈ R0 and n ∈ R
X O F = E
F O X = E
(am, bm + n) = (1, 0) and (ma, na + b) = (1, 0)
Considering (am, bm + n) = (1, 0)
am = 1
m = 1/a
And bm + n = 0
n = -b/a [since m = 1/a]
Considering (ma, na + b) = (1, 0)
ma = 1
m = 1/a
And na + b = 0
n = -b/a
Hence, the inverse of (a, b) ∈ A with respect to O is (1/a, -b/a)