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

Which is the rope you never skip with?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?

You enter your friend's room. He is not in his room. Although you see that on the bed there are two dogs, five cats, two giraffes and three pigs. Also, a couple of chickens and ducks are flying in the room.

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How come ?

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I am an odd number. Take away a letter and I become even. What number am I?