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

A cat, a dog and a monkey were stolen. 3 suspects got caught: Harish, Manoj and Tarun. All we know is each person stole one animal, but we do not know who stole which. Here are the investigation statements. Harish said: Tarun stole the cat. Manoj said: Tarun stole the dog. Tarun said: They both were lying. I did not steal the cat or the dog. Later on, the police found out the man who stole the monkey told a lie. The man who stole the cat told the truth. Can you find out who stole which?

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

A Doctor always sneezes before the rain. Doctor sneezes, Will it rain?

How can you leave a room with two legs and return with six legs?

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

Lifeless eyes on my smiling face and watch your child's sleeping place. In their dreams they hold me tight. What am I?

What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see?

Find three numbers such that When we multiply three numbers, we will get the prime numbers. The difference between the second and the first number is equal to the third and second.

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?