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

He does not have any heart but still, He manages to live.
If you kill him, you will eventually die but yet you kill him.
He cannot run, who is He?

Rose, Lily and Jasmine decided to buy flowers for their moms on Mother's Day. One of them bought lilies, the other roses, and the third one jasmines.
'It's funny!' said the girl with roses, 'we bought roses, jasmines and lilies, but none of us bought the flowers matching her name'.
'You're right!', said Lily.
What kind of flowers did each of the girls buy?

You are given with the following sum. Each of the letters can be decoded as a digit. If we tell you that D = 5, then can you solve it entirely?

DONALD
+GERALD
=ROBERT

In a secret society, a buried chamber can be accessed only via a secret password. The password is seven characters long and comprises of just letters and numbers.

You find a code that can help you in cracking the password. The code says "You force heaven to be empty".

Can you deduce the password from that?

Can you solve the below algebraic mathematical equation?

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

There was a blind man. He had four socks in his drawer either black or white. He opened it and took out two socks. Now the probability that it was a pair of white socks is 1/2.

Can you find out the probability that he had taken out a pair of black socks ?

My location can be determined by the below rebus.
So where am i ?

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?

Count The number of F's in the paragraph below:

"FINISHED FILES ARE THE RESULT OF YEARS OF SCIENTIFIC STUDY COMBINED WITH THE EXPERIENCE OF YEARS"