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

One of the leprechaun is missing if you see the two pictures attached to this question. Where did he go? When he comes back, do you know where has he been?

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

what one word does the below rebus identifies?

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?

It has a long neck, A name of a bird, Feeds on cargo of ships, It's not alive,

What is it?

A woman is sitting in her hotel room and hears a knock at the door. She opens the door to see a man whom she’s never met before. He says, “I’m sorry, I have made a mistake, I thought this was my room.” He then goes down the corridor and into the elevator. The woman goes back into her room and calls security. What made the woman so suspicious of the man?

This is a most unusual paragraph. How quickly can you find out what is so unusual about it? It looks so ordinary, you'd think nothing was wrong with it. Actually, nothing IS wrong with it. But it is not as ordinary as you might think. If you think about it for a bit, you will find out why it is truly so unusual. So what is it? What is so unordinary about this paragraph?

What has lots of eyes, but can’t see?

There is an exact a week gap between Christmas and New Year. Hence, It is obvious that the new year that comes right after Christmas comes on the same day of the week.

A Strange thing happened in the Year 1777. Christmas occurs on Wednesday and New Year on Monday. How is that possible?