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

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

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

? : 3839 :: 11 : 1209

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

Krish is 45 years old and his mother Crishtina is 73 years old.

Can you find out how many years ago, his mother was three times his age?

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?

Find the combined weight of the Cat, Dog and Rabbit in the given picture.

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

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