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 am white when I am dirty, and black when I am clean. What am I?

A bomb goes off.
Carnage.
One person, only a few feet away, survives! How can this be?

Three people are in a room. Ronni looks at the Nile. The Nile looks at Senthil. Ronni is married but Senthil is not married. At any point, is a married person looking at an unmarried person? Yes, No or Cannot be determined.

Can it be possible to build a house that has all its four walls facing towards the South?

We have four gears with below features=> Both Gear A and D has 60 teeth=> Gear B has 40 teeth=> Gear C has 20 teeth=> Every two minutes, Gear B makes 25 full turns.What is the relative speed of Gear A and Gear B?

If a boy blows 18 bubbles,
Then pops 6 eats 7 and then
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How many are left?

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(it's a funny riddle)

Can you divide the below-given shape into four equal and identical pieces?

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