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

In the picture that is attached with this question, you can find a square which comprises of four little squares inside it. Consider this square to be made with matchsticks. You have to remove two matchsticks such that only two squares remain instead of five.How will you do it ?

In the below-given picture of a pretty girl, there is something wrong. Can you find out what it is?

Sally lives in a place where six months of the year is mild summer and the temperature drops significantly the other six months. She owns a lake where there is a small island. She wants to build a house on the island and needs to get materials there. She doesn’t have a boat, plane, or anything to transport them to the island. How does Sally solve this problem?

A container contains 100 eggs. They can be either fresh or rotten. What is sure is the fact that there is at least one fresh egg in that container.

If you are asked to pick two eggs randomly from the container, at least one of them will be rotten.

Can you calculate how many eggs in that container are fresh?

If you say my name, I will no longer exist. What am I?

What's the next in the series?

H, Be, F, S, Mn, Kr, In, Gd, Tl, ?

Can you find out the missing number?

? 4 5 3 5

9 5 7 10 3

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

Can you find the 09 errors in the picture below?