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

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?

You are given with the following sum. Each of the letters can be decoded as a digit. If we tell you that D = 5, then can you solve it entirely?

DONALD
+GERALD
=ROBERT

How can you write nineteen in a manner that if we take out one, it becomes twenty?

Can you place six X (crosses) in below board without making three in a row in any way ?

Three ants are going up a hill, one behind the other. The last ant then says to the other ants, 'There is an ant behind me!'' How come?

The Judge knows that Alamgir was killed by his girlfriend Jasline, but the judge is unsure whether to punish her. Why?

There is a wide field of corn. A goose finds its way into the field and starts running. Can you find out till which point the goose can run into the field?

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?