Can you solve below mathematical equation?

2^1234 - 2^1233

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

No one wants to have it, but if one got it, he does not want to lose it. What is It?

There is a place where if I stand up straight, I will still be considered sideways.

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

My cousin lives in one story house in Antarctica. His house is made the of-of sandstone. what is the color of stairs?

I am never scared but became petrified and can’t live in a house but would die to make one. What am I?

In the image given, you can find several triangles. Can you count them all?

I am a ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?