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

Mr Red Lives in the red house.
Mr Green Lives in the greenhouse.
Mr Yellow Lives in the yellow house.

Who lives in the Whitehouse?

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?

There was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?

How will you measure 15 minutes using two hourglasses of 7 minutes and 11 minutes respectively?

Our product and our sum always give the same answer. Who are we?

An inspection by the superintendent of St. Joseph School was scheduled on the next day. The class teacher Jenifer knew that he would be asking questions from her class and she would have to choose a pupil to answer. To offer a perfect impression over him, the teacher explained certain instructions to the students to maximise the chances of getting correct answer every time.

What did she say to the students?

500 women soldiers are arranged in an array of ten rows and fifty columns in accordance with their respective heights. Now, the tallest woman from each row is asked to move out in the front. From them, the shortest one is labelled as Alpha. They are then asked to resume their original position.

Now, the shortest woman in each column is asked to come out in front. The tallest among them is labelled as Beta.

Can you find out if Alpha will be taller or Beta?

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

Given below is simple addition with a defined pattern pattern:
7 + 7 = 2
8 + 8 = 4
8 + 5 = 1
6 + 9 = 3
10 + 11 = 9

Can you analyze the pattern and find out the answer for:

4 + 9 = ?