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 man is trapped in a room. The room has only two possible exits doors. Through the first door there is a room constructed from magnifying glass. The blazing hot sun instantly fries anything or anyone that enters. Through the second door there is a fire-breathing dragon. How does the man escape?

Two friends Smith and Andrew were talking about the bravery of their families. Smith told great stories about his courageous grandfather who fought for Britain in "World War I". Andrew told that his grandfather was so brave that in 1919 just after the war he was honoured with a bravery medal with the words "For our Courageous Soldiers In World War I" embedded into it. Smith knows that his friend is lying. How?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

Find the missing number in the series below

13 -21 34 -55 ? -144

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

A patient was diagnosed with some ailment. He was given five different tablets to take at night at an interval of 15 minutes.

How long will it take the patient to consume all the five tablets?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

John needs to purchase 100 chocolates from three different shops and he has exactly 100 rupees to do that which he must spend entirely. He must buy at least 1 Chocolate from each shop.

The first shop is selling each chocolate at 5 paise, the second is selling at 1 rupee and the third is selling at 5 rupees.

How many chocolates should he buy from each shop?

Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.

"Are you twins," ask the headmaster.
"No," replies the boys.

Is it possible?