Can all amino acids in proteins ionize?

[Windpt21]

I just had a final exam in a course and am perplexed by an answer the questions was:

Amino Acids found in Protiens:

One of the answers was: cannot all ionize

I felt like that was a correct answer but got the question incorrect, what do you guys think?

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[quackwhacker]

The COOH and NH3 in each AA can ionize