Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

Keyboard words are not in alphabetical order, Why?

I have one of the three numbers: 1, 2, or 3 in my mind. I speak only truth. You can ask me just one question for which I will only reply in yes or no or don't know. What question will you ask from me so that you are able to know the number?

Two girls were born to the same mother, on the same day, at the same time, in the same month and year and yet they're not twins. How can this be ?

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How can you make the metal ring drop to the bottom if you are not allowed to touch anything - not the bottle, not the cork, not the thread and not the ring?

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10+10 and 11+11 can give you the same answer.

Explain how?

What are the 50th, 63rd and 100th numbers in the sequence below?
4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...