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

A man dies of old age on his 25 birthday. How is this possible?

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

A train leaves from point A for point B at 80 mph. After half an hour, another train leaves from point B for point A at 60 mph.

Which of the trains will be farther from point A when they meet ?

Can you find the missing letter in the sequence?
S - T - I - L - ? - T - F - Y - C

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

I cry without having a voice.
I fly without having wings.
I bite without having teeth.
I whisper without a mouth.

Who am I?

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

A man looks at a painting in a museum and says, “Brothers and sisters I have none, but that man’s father is my father’s son.” Who is in the painting?