The formation of water from ${\mathrm{H}}_{2\left(g\right)}$ and ${\mathrm{O}}_{2\left(g\right)}$ is an exothermic reaction because

Exothermic reaction is the chemical reaction in which energy is released.

Here, $\Delta H$ (enthalpy) = product energy - reactant energy

The value of (product energy -reactant energy) $<0$.

So, the chemical energy of $H_{2\left(g\right)}$ and $O_{2\left(g\right)}$ are high and it is higher than water.

Therefore, option $\left(\mathrm{A}\right)$ is correct.