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

Can you find out which number multiplied by itself will give the output as 12345678987654321?

A 52% bias toss for head using the 51% tail bias coin was done to obtain a fair result.

Can you find how bias is the floor in this case?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

Can you solve below mathematical equation?

2^1234 - 2^1233

John needs to purchase 100 chocolates from three different shops and he has exactly 100 rupees to do that which he must spend entirely. He must buy at least 1 Chocolate from each shop.

The first shop is selling each chocolate at 5 paise, the second is selling at 1 rupee and the third is selling at 5 rupees.

How many chocolates should he buy from each shop?

'S' refers to the number of seconds in a day and 'H' refers to the number of hours in ten years. Which quantity out of these two is greater?