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 plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?

There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

Replace the question mark with the correct number below.

What does this rebus riddle means ?

What is in seasons, seconds, centuries and minutes but not in decades, years or days?

It is deaf, Dumb and Blind!!!

Still, always tells the truth. What is it?

Find the number of squares in the below picture

John has played 50 ODI's and his average is 50. How many runs should he score in his 51st ODI, so that his average score jumps to 51?

The following "Brain Bat" means Slow Down.
S
L
O
W

Using the same logic, can you tell us what does the following Brain Bat means ?
E
V
I
G