Step 1: Understanding laughing gas.
Laughing gas is the common name for nitrous oxide, which is widely used as an anesthetic and analgesic in medical and dental procedures.
Step 2: Chemical identity.
Nitrous oxide has the molecular formula $\mathrm{N_2O}$ and is distinct from other nitrogen oxides like $\mathrm{N_2O_3}$, $\mathrm{N_2O_4}$, and $\mathrm{N_2O_5}$.
Step 3: Conclusion.
Hence, the correct answer is (A) $\mathrm{N_2O$}.