We multiply infinity by infinity, and what will be the final answer?

The answer will be infinity.

Infinity is not a number. It's much much greater than the largest number you can think of.

Infinity operations are important while solving limits.

Infinity + infinity= infinity

Infinity - infinity = not defined

Infinity × infinity = infinity

Infinity ÷ infinity = not defined.

We multiply infinity by infinity, and what will be the final answer? 

Infinity is a concept, not a number.  It cannot be used in multiplication.  

All true, however, there are different 'degrees' of infinity.   My wording is probably not correct.

\(\displaystyle \lim_{x\rightarrow \infty}\;\;3x=\infty \\ \displaystyle \lim_{x\rightarrow \infty}\;\;x=\infty \\ but\\ \displaystyle \lim_{x\rightarrow \infty}\;\;\frac{3x}{x}=3\)