How do I find all the bases which $11^2 < 122$ is correct for them?

Question

I tried to go all over the bases but it doesn't work well. I don't know how to present multiplying in general... I believe I somehow have to compute 11 times 11 in every base and convert it to decimal number and check if it bigger than 122. Any thoughts?

Answer 1

If the basis is greater than two, then $$\begin{array}{ccc} &1&1\\ \times&1&1\\ \hline &1&1\\ 1&1\\ \hline 1&2&1 \end{array}$$