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

Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?

15 caves are arranged in a circle at the temple of doom. One of these caves has the treasure of gems and wealth. Each day the treasure keepers can move the treasure to an adjacent cave or can keep it in the same cave. Every day two treasure seekers visit the place and have enough time to enter any two caves of their choice.

How do the treasure seekers ensure that they find the treasure in the minimum number of possible days?

In Greek mythology, the Sphinx sat outside of Thebes and asked this riddle of all travellers who passed by. If the traveller failed to solve the riddle, then the Sphinx killed him/her. And if the traveller answered the riddle correctly, then the Sphinx would destroy herself. The riddle:

What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?

Oedipus solved the riddle, and the Sphinx destroyed herself.

The owner of a popular clothing store comes up with his own method of pricing items. A vest costs $8, socks cost $10, a tie costs $6, and a blouse costs $12. Using the owner’s method, how much would a pair of underwear cost?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

In which direction should the missing arrow point?

I cannot talk, but I always reply when spoken to. What am I?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?