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

I am an odd number. Take away a letter and I become even. What number am I?

What's a single-digit number with no value?

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

An express train takes 3 seconds to enter the tunnel which is 1 km long.
If it is travelling at 120 km an hour, how long will it take to pass completely through the tunnel?

Can you make the number 24 by utilizing the numbers 1, 3, 4 and 6? You must use one number only one time and you can use mathematical operation symbols anytime anywhere.

Using mathematical symbols like +, -, and x in order to make the equations correct. Replace # with the above-given symbols.

9 # 8 # 7 # 6 # 5 # 4 = 91

There once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

A brand new Mobile Phone was on sale at 20% as a promotional offer. By what per cent must the Mobile price be increased to sell it at the original price again?

Can you solve below mathematical equation?

2^1234 - 2^1233