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

If we add four times the age of John four years from now to five times his age five years from now we get ten times his current age.

How old will John be two years from now?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

There are two candles. Both will only burn exactly for an hour. How will you use these two candles to measure forty-five minutes?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

Can you write down eight eights so that they add up to one thousand?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

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

Can you solve below mathematical equation?

2^1234 - 2^1233