How to identify a pseudo-first-order reaction?
There are four steps:


Identify the mechanism.
Find the rate-determining step.
Write the corresponding rate equation according to the stoichiometric coefficients of that step.
Remove abundant reactants.


1. Identify the mechanism



Assuming that there is no acid to catalyze the reaction, it proceeds via a nucleophilic addition/elimination reaction.

An acetic anhydride molecule $(1)$ is attacked by the lone pairs on the water to form the complex $(2)$. This is the addition step.

The complex tautomerizes to give $(3)$, which is converted to our products, namely 2 acetic acid molecules $(4)$. This is the elimination step.

2. Find the rate-determining step.

Presumably, it is the first step.

3. Write the rate equation.

In the first step, one molecule of acetic anhydride reacts with one molecule of water. Therefore, it is a first-order reaction with respect to both of them:


$\text{Rate} = k [\ce{Ac2O}] [\ce{H2O}]$


4. Remove abundant reactants.

Water is abundant, so it is removed from the equation:


$\text{Rate} = k [\ce{Ac2O}]$


Conclusion

It is a pseudo-first-order reaction [A].