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

There is a river to cross using a river raft and there are eight people (father, mother, policeman, thief, 2 daughters and 2 sons). No one knows to operate the raft except the adults and also excluding the thief. Only two people can go in the raft at a time. The raft should keep coming back and forth in order to pick and drop the people.
Rules to be followed:
Father: the father cannot stay in the raft or outside the raft without the presence of the mother.
Mother: the mother cannot stay in the raft or outside the rat without the presence of the father.
Thief: the thief is not allowed to stay with any of the family members unless there is a policeman.
Policeman: the policeman can travel with anyone.
2 sons and 2 daughters: they are not allowed to travel in the raft without the presence of an adult. They cannot either travel in the presence of only thieves without the policeman. The sons cannot be with their mothers without their father's supervision. The daughters are not allowed to be there with their fathers without the supervision of their mothers. But the daughters and the sons can be left unsupervised (as long as the other rules are applied).
What is the sequence that the people should follow in order to cross the river through the raft keeping in mind all the rules?
The rules are applicable not only in the raft but also outside the raft.

A bank customer had $100 in his account. He then made 6 withdrawals. He kept a record of these withdrawals, and the balance remaining in the account, as follows:

Withdrawals Balance left
$50 $50
$25 $25
$10 $15
$8 $7
$5 $2
$2 $0
----- -----
$100 $99

Why are the Totals not tallying?

Who are the happiest people in IPL match?

An ant is travelling on a 1-meter-long rope at 1 cm/second but also the entire rope is being stretched by an extra 1 meter/second. Is it possible for the ant to reach at the end of the rope?

What do you see in the image below

Can you find out which triangle will have a bigger area among the following?
1. A triangle with sides 300, 400 and 500
2. A triangle with sides 300, 400 and 700

I have no life, but I can die. What am I?

The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.

"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything.

"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell.

"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead.

"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'

"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"

What is the strategy they come up with so that they can be free?

Teacher ask the student

'Why are you standing on that chair in music class ?'.

what did student replied ?