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

I don't get anymore wetter, no matter how much rain falls on me.

Christina has four daughters, and each of her daughters has a brother. How many children does Christina have?

What's the only room from which no one can enter or leave

There are three houses in a straight row. One is red, one is blue, and one is white. The red house is left of the middle. The blue house is right of the middle. Where's the white house?

In one of the popular batman series movie "Batman Forever", there was a riddle that goes like "Tear me off and then scratch my head and I was red then and now I am back. Who am I?

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

I am working in a bus company. The company recently went under expansion and therefore there was not enough room for all the buses. As a result, twelve buses had to be stored outside.

If the company decides to expand the garage space by forty percent, enough space to accommodate the current buses will be created leaving enough space for twelve more buses if the need arises in future.

Can you calculate the number of buses that the company owns at present?

What goes through cities and fields, but never moves?

Your job is to measure 45 minutes if you have only two cords and matches to light the cords.

1. The two cords are twisted from various materials, so their different segments can burn at different rates.
2. Each cord burns from end to end in exactly one hour.

Describe your way of measuring the 45 minutes.