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 doctor and a boy were fishing. The boy was the doctor’s son, but the doctor was not the boy’s father. Who was the doctor?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

Krish is 45 years old and his mother Crishtina is 73 years old.

Can you find out how many years ago, his mother was three times his age?

I’m orange, I wear a green hat and I sound like a parrot. What am I?

What has hands, but can’t clap?

If eleven plus two equals one, what does nine plus five equal?

You need to arrange three 7 and mathematical symbols to form number 1?

A Scientist was fifty years old in the year 2000 but he was forty years old in the year 2010. How can this be possible?

PS: It has a logical answer.