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

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

Which word does the below Plexor means ?

What does this simple rebus mean?

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99

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 number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

It has five wheels, though often think four, You cannot use it without that one more, You can put things in it, you can strap things on top, You can't find it in the market, but you can still go shop. What is it?

In a rainy season, one day 3 huge ladies walked under a normal-sized umbrella.
The umbrella is not huge enough to accommodate all 3 ladies yet not a single lady got wet. Why?