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

Move three sticks of the spiral below to form a square.

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

The product of three consecutive numbers is 7980.
Then the sum of these consecutive numbers would be?

What is the next shape from answers A, B, C, and D figure?

See the given image carefully. What you have to do is move the blue checkers in the position of the black checkers and vice versa. You are only allowed to move the checker to an adjacent empty space. Do it in the least possible moves.

The doctor advised his patient to take a tablet after every fifteen minutes. He gave him five tablets in total.

How much time will he take to have all the five tablets?

A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say the last sentence to determine how the penalty will be carried out. If the thief lies, he will be hanged, if he speaks the truth he will be beheaded. The thief tells the last sentence and to everybody's surprise some minutes later he is set free because the judge cannot determine his penalty. What did the thief say?

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

A pregnant woman is preparing to name her seventh child. Her children's names so far are Dominique, Regis, Michelle, Fawn, Sophie, and Lara. What will she name her next child -- Jessica, Katie, Abby or Tilly?