A non-reducing sugar A hydrolyses to give two reducing mono saccharides. Sugar A is:

A non-reducing sugar is one that does not have a free anomeric carbon (hemiacetal or hemiketal group) and therefore cannot reduce Fehling's or Tollens' reagent. Among common sugars, sucrose is the classic non-reducing sugar because the glycosidic bond in sucrose is formed between the anomeric carbons of both glucose and fructose (C-1 of glucose and C-2 of fructose), leaving no free reducing group.

When sucrose is hydrolysed (by dilute acid or the enzyme invertase), it breaks down into its two monosaccharide units: $$\text{Sucrose} + \text{H}_2\text{O} \rightarrow \text{Glucose} + \text{Fructose}$$. Both glucose and fructose are reducing sugars, as each has a free anomeric carbon after the glycosidic bond is cleaved.

The other options — fructose, galactose, and glucose — are all monosaccharides. They are already the simplest sugar units and cannot hydrolyse further into two reducing monosaccharides. Moreover, all three are themselves reducing sugars, not non-reducing.

Therefore the answer is Sucrose, which is Option D.