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 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?

Can you solve below mathematical equation?

2^1234 - 2^1233

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

Replace each alphabet with the number (1-9) to make the below equation correct.

AB * C = DE - F = GH / I

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

Solve below popular number sequence
314 159 265 358 979 323 846 ?

Three brothers Jacob, John, and James live in Mexico City. The product of the ages of these brothers is 175. Jacob and John are twins. How old is James?