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

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?

2 ladies and 2 girls need to cross a river in a boat big enough for 1 LADY or 2 girls. How do they do it?

I organized a small get together at my home.
In the party , i have a barrel with some whiskey in it.

Suddenly Guest 1 say 'I bet this barrel of whiskey is more than half full'.
'No, it's less than half full' Guest 2 replied.

I don't have any measuring instrument and without removing whiskey from it , how can i determine which of the guest is right ?

An equation has been laid down using a few matchsticks. However, as you can see, the equation is not correct. Can you correct the equation if you are allowed to add or remove 5 matchsticks?

Find the number of squares in the below-given picture.

There are nine dots in the picture that has been attached with this question. Can you join all the dots by drawing four straight lines without picking up your pen?

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

What does below rebus means ?

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.