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 tank will fill first?

Two fathers and two sons decided to go to a shop and buy some sweets upon reaching. Each of them bought 1 kg of sweet. All of them returned home after some time and found out that they had 3kg of sweets with them.

They did not eat the sweets in the way, nor threw or lose anything. Then, how can this be possible?

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

What always comes into a house through the keyhole?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

How many words can a pen with half refill write?

There was a greenhouse.
Inside the greenhouse, there is a white house.
Inside the white house, there is a red house.
Inside the red house, there are lots of babies.

What is It?

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly

The world's largest Thanksgiving turkey was on display at a fair. Everyone was admiring it when suddenly a woman ran up and shot the turkey and left. Everyone knew her yet nobody made any attempts to stop or report her. Why?