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 who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

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 = ?

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

This is a picture puzzle. You have to guess the name of the movie that can be related to the picture.

Can you name an animal whose killing cannot be performed without spilling your own blood?

On her drawing table, Sayna lit 12 coloured candles. A few seconds later she blew two candles off.

How many candles Sayna have at the end?

The dirtier I get, the whiter I look. Who am I?

An old Woman left INR 33,333 to be divided equally among two fathers and two sons and each was to receive INR 11,111.
How was this possible?

Can you find out which number multiplied by itself will give the output as 12345678987654321?