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 little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

A brand new Mobile Phone was on sale at 20% as a promotional offer. By what per cent must the Mobile price be increased to sell it at the original price again?

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

Can you calculate the probability of getting a sum of six when a dice is thrown twice?

Find three numbers such that When we multiply three numbers, we will get the prime numbers. The difference between the second and the first number is equal to the third and second.

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

John can place six large boxes or nine small boxes into a carton.

Can you find out in how many cartons can he place sixty-six boxes in total?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?