The IUPAC name of ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{CHCH}}_3$ is
 

The given compound is an alkane.

IUPAC rules for naming alkanes:

1.     The name of an alkane ends with “ane”.

2.     Choose the longest carbon chain for the root name.

3.     Identify the substituents.

4.     Number the carbon atoms on this longest chain such that the substituents gets the lowest number.

5.     If the same substituent appears more than once, then the prefix (di, tri, tetra) is used to indicate their frequency.

6.     If there are more than 2 substituents, they are named in alphabetical order with the position written ahead of them.

Example- 2-methylbutane or 2-ethyl-4-methyl-heptane.

Thus, the structure of the given compound is-

Hence, it is named 2-methylpropane.

Hence, option A is correct.