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

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

At a Society election for president, precisely 963 votes were cast.
There is a total of 4 candidates that participate in the election.

The winning candidate exceeds the opponents by 53, 79 and 105 votes.

How many votes do each candidate gets?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

Replace the question mark with the correct number in below Picture:

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

Joseph buys three kinds of chocolates for 100 rupees. The first one is priced at 5 rupees, second one at 3 rupees and third one at 0.5 rupees.

If he bought 100 chocolates in total, how many pieces do you think he bought each chocolate?

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

You need to arrange three 7 and mathematical symbols to form number 1?