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 word I know has six letters it contains, remove one letter and 12 remain. What is it?

In an office's desk, you find a unique method that shows the current day of the month. Two numbered cubes are used to depict the current date.

Can you find out the numbers on both the cubes so that each date can be mentioned using them?

Please note that you have to use both the cubes to display any date. Thus the 1st day must be represented by 01 and so on.

John is looking at Jenifer, but Jenifer is looking at Jacob. John is married, but Jacob is not.

Is a married person looking at an unmarried person ?

"That Restaurant always remains crowded. This is the reason why nobody goes there".

Can you find a flaw in this statement?

How can you make the following equation true by drawing only one straight line: 5+5+5=550 ?

Jack was having a candle light dinner with his girlfriend. Suddenly a cold gush of wind entered through the open window and three of the ten candles were extinguished. Assuming that none of the other candles were extinguished.

How many candles are they left with in the end ?

A man stands on one side of a river, his dog on the other. The man calls his dog, who immediately crosses the river without getting wet and without using a bridge or a boat. How did the dog do it?

Mr Red Lives in the red house.
Mr Green Lives in the greenhouse.
Mr Yellow Lives in the yellow house.

Who lives in the Whitehouse?

A man started to town with a fox, a goose, and a sack of corn. He came to a stream which he had to cross in a tiny boat. He could only take one across at a time. He could not leave the fox alone with the goose or the goose alone with the corn. How did he get them all safely over the stream?