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

If we change the South-East direction into North and North-East into West and all others similarly.
Can you find out which direction will be in the place of South-West direction?

A certain street contains 100 buildings. They are numbered from 1 to 100. How many 9's are used in these numbers?

I hide my treasure in the ground, my tail is big and fluffy. If you spot me in a tree, please don’t call me scruffy. What am I?

You board a train. The train will have to enter a tunnel soon. You are claustrophobic. Which place is the best for you to sit?

What part of the chicken has the most feathers?

If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

I know a nine-letter word having only one vowel.
Do you ?