Does It Always Hold?

Algebra Level 3

$\begin{array} {r c r c l } 1 &\times & 1 & = &1 \\ 11 & \times& 11 & = &121 \\ 111 & \times& 111 & =& 12321 \\ 1111 & \times& 1111 & =& 1234321 \\ \end{array}$

Observe the equations above.

Hence, what is the value of

$\underbrace{1111111111}_{10 \text{ 1's } } \times \underbrace{1111111111}_{10 \text{ 1's } } \; ?$

Inspiration.