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

What is the largest number you can write with just 3 digits?

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

Name a key which is hardest to turn.

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

A girl says this to her best friend: “I was born in 1955, and I celebrated my 17th birthday last weekend.” Her best friend thinks she’s lying, but she’s actually correct. How is that possible?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

While handling a project, the landscaper is asked by the owner of the mansion that he wants four trees in front of his mansion that are exactly equidistant from each other.

How will he do it?

John is a strange liar.

He lies on six days of the week, but on the seventh day, he always tells the truth.

He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."
Day 2: "Today, it"s Thursday, Saturday, or Sunday."
Day 3: "I lie on Wednesday and Friday."

On which day does John tell the truth?