We need to identify the disaccharide/polysaccharide which on hydrolysis gives D-Galactose and D-Glucose.

Check each option:

A: Amylose
Amylose is a polysaccharide made only of repeating D-glucose units.
On hydrolysis, it gives only D-glucose, not galactose.
So, A is incorrect.

B: Sucrose
Sucrose on hydrolysis gives D-glucose + D-fructose.
It does not give galactose.
So, B is incorrect.

C: Maltose
Maltose consists of two D-glucose units.
On hydrolysis, it gives D-glucose + D-glucose.
So, C is incorrect.

D: Lactose
Lactose is a disaccharide composed of D-galactose + D-glucose.
On hydrolysis: $\text{Lactose} \xrightarrow{\text{hydrolysis}} \text{D-galactose} + \text{D-glucose}$ So, D is correct.

Therefore, the compound $A$ is: $\boxed{\text{Lactose}}$