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 barrel with no lid and some wine in it. 'This barrel of wine is more than half full,' said Curly. 'No it's not,' says Mo. 'It's less than half full.' Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?

Pronounced as 1 letter, And written with 3, 2 letters there are, and 2 only in me. I’m double, I’m single, I’m black blue and grey, I’m read from both ends, and the same either way. What am I?

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

A Car driver was heading down a street in Washington. He went right past a stop sign without stopping, he turned left where there was a 'no left turn' sign and he went the wrong way on a one-way street. Then he went on the right side of the road past a cop car. Still, he didn't break any traffic laws. Why not?

They do not possess flesh or feathers or scales or bone
But still, they are blessed with fingers and thumbs of their own.

A Car is crossing a bridge 2 miles long. The bridge can only hold 10000 lbs, which is the exact weight of the car. The Car makes it half way across the bridge and stops. A bird lands on the car. Does the bridge collapse? Explain.

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

Two-person want to cross a river. Only one boat is present on the riverside that can carry only one person at a time.

However, they still manage to cross the river. How is it possible?

There was a strange boy who was born before his father. How can this be possible?