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

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

John and his wife were living in a rural place. On a particular day, John's wife fell ill and he called the local doctor. When the doctor picked up, he said, "Doctor, my wife is ill. She might have appendicitis."

"This can't be possible! I took out her appendix two years ago myself," the doctor explained.

When diagnosed, John's wife was found to have appendicitis. How can this be possible?

1 dollar = 100 cent
= 10 cent x 10 cent
= 1/10 dollar x 1/10 dollar
= 1/100 dollar
= 1 cent

=> 1 dollar = 1 cent

solve this tricky problem?

Can you identify the Oscar-winning movie from the rebus below?

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

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?

Get total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator.
Do you ?

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?