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

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

What kind of tree can you carry in your hand?

In the Thar desert, 3 men found a big 24L Jar is full of water. Since there is a shortage of water so they decided to distribute the water among themselves such that they all have equal amounts of it. But they only have a 13L, a 5L and an 11-litre Jar.

How do they do it?

Which Number is the odd one out?

A) 7145
B) 2716
C) 5321
D) 4135

The husband and wife were jogging in the morning. To match every two steps of the husband, the wife required three steps. If Both of them start with the here right foot. After how many steps do their left foot be together?

I am 5 letters long.
My first two tell you who I am
My first 3 could be a medicine
My last three reversed could be a young boy.
My 4th, 3rd and 2nd in that order could be a fruit drink.
If you have me you may hang me round your neck
WHAT AM I ?

There were three women in all the swimming costumes!
One was happy and the other two were sad!
The happy one was crying and the sad ones were smiling.
Why was this?

There was once a troop of 5 elves. The 5 elves were very dedicated on finding the magical treasure of 1000 coins. However, being elves, they were super geniuses, very greedy and they did not hesitate in taking lives of other elves. The 5 elves were named Aye, Bee, Cee, Dee and Ee, ranked from high to low respectively, from Aye to Ee. One fine day, their efforts brought results and they found 1000 coins. Now they had to split it in between them as per their ranks. The lowest ranked elf has to make the proposal. If the proposal is accepted by majority, it is agreed, or the suggesting elf is killed.

What proposal should elf Ee make ?