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 can hear me, but you can't touch or see me.

What am I?

There are three houses in a straight row. One is red, one is blue, and one is white. The red house is left of the middle. The blue house is right of the middle. Where's the white house?

Andrew sees a very rare bird named "Ruppell's vulture". Soon Andrew was dead. Can you explain the mystery, Mr. Sherlock?

If I remove one from eleven it becomes Ten and if I remove one from nine also becomes Ten. How?

One day, John and his friends were playing around. Jacob hit something with a Pin and it popped. John's dad came into the room that very moment, but he wasn't mad. In fact, he was smiling. What did Jacob hit?

Count the number of triangles in the given picture.

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

John went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
He went again to the parrot shop and complaint to the shopkeeper, but the shopkeeper never lied. Explain?