Is unsystematic risk eliminated when beta is 1

When beta is 0, systematic risk is eliminated.

What if beta is 1, is unsystematic risk eliminated?

No.

If systematic risk is to be removed, what should beta be?

Zero, as you wrote above.

Apologize for my typo…

Actually I mean if unsystematic risk is to be removed, what should beta be?

Beta doesn’t tell you about unsystematic risk.

The more you diversify a portfolio, the more you reduce unsystematic risk, not sure you can eliminate it.

The common wisdom is that with about 30 (carefully chosen) securities, you can eliminate systematic risk.

But it has nothing to do with beta.

Or by using a market neutral strategy (alpha strategy)