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

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

Five lovely ladies(Sophia, Isabella, Madison, Emma and Olivia) planned a picnic.

They each buy one thing each for the picnic.

Sophia, Emma and Olivia got a drink : orange-Juice, apple-juice, and mango-juice.
Olivia got the drink with the same letter as the one in her first name.
Emma loves mango-juice.
The other two bring some food : chocolates and pizza.
Also Madison is allergic to cheese.

So which ladies bought what ?

I add 5 to 9 and get 2. The answer is correct, so what am I?

The current time can be represented by below textual rebus.

0
=========
B.Sc
LLB

Can you tell us the current time?

Can you find the next number in the below sequence
3 , 7 , 10 , 11 , 12 , 17 ?

You are given 2 eggs.
You have access to a 100-storey building.
Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100th floor, Both eggs are identical.
You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

The barber of Town shaves all men living in the town. No man living in the town is allowed to shave himself. The barber lives in that town. Who then shaves the barber of the town?

Complete the following series. It.s very logical:

1, 4, 5, 6, 7, 9, 11, __?

Which is faster, Heat or Cold ? Explain.