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

There is a wide field of corn. A goose finds its way into the field and starts running. Can you find out till which point the goose can run into the field?

A crime was committed at baker street. Ibrahim Dakota who was shot in the stomach was the main suspect. Sherlock questioned the suspect. The conversation started as:
Sherlock: What's your story, Ibrahim?
Ibrahim: I was walking around baker street and suddenly a man from the back shot me. I ran as fast as I could to save my life".
Sherlock: That is enough (and ask the police to arrest him).

Why does Sherlock think he is the murderer?

Can you write down eight eights so that they add up to one thousand?

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

The more you take me, the more you leave me behind.
Who Am I?

I shave every day, but my beard stays the same. What am I?

What four weights can be used to balance from 1 to 30 pounds?

Whats the next number in the below number sequence pattern.

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?