Mathematics the cross product of perpendicular vectors

Hey! Trying to do this maths question but completely stuck on how to prove that it is false algebraically? The question is:
a is perpendicular to b therefore a x b = 0 and I need to prove that if a and b are perpendicular then the cross products of them do not equal 0.
Thank you so much!

Can you post the original question(s). Have you covered the magnitude formula |a||b|sin(theta)?

Link for the question: file:///C:/Users/shiva/Downloads/Teach_VectorsProds_TrueFalse.pdf
Its the first one on the second column and we've been asked to prove if they're true or false using algebra or reason, not using numbers. And yep I have covered the magnitude formula

Ah its not letting me upload it sorry! All the question says though is:
a is perpendicular to b therefore a x b = 0
Prove whether this statement is true or false using algebra or another non-numerical method.