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

Two guards were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, "Why are you smiling?"

How did he know his companion was smiling?

A person is found murdered in his Chamber. When the crime scene is investigated, the Investigator find out that there is a calendar on which the victim has written a few numbers with his blood. The numbers are 4, 11, 11 and 4.

There are four suspects in the murder, John, Jacob, Anna and Lee. Can you find out who is the murderer?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

Find the Goldfish below the given Image.

He loves to dance, twist and prance, he shakes his tail, and as a way he sails, wingless he flies into the sky. What is he?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

Take number 1000 and then add 20 to it.
Now add 1000 one more time.
Now add 30.
Now add 1000 one more time.
Now add 40.
Now add 1000 one more time.
Now add 10.

What is the total?

After a heavy Thanksgiving meal, the night watchman went to work. In the morning, he told his boss he had dreamed that a saboteur planted a bomb in the factory and that he felt it was a warning. The boss promptly fired him. Worker confused, Why boss fire him?