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

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

On 26-01-2022, Juli was murdered at her house in a city in India in the afternoon. There were three suspects in the murder and the following are the statements that were given by them:

John: I visited my village that day.
Jacob: I was out to deposit my house tax in the municipality office at that time.
Jonny: I was at a friend's place having lunch at that time.

Can you find out who is the murderer?

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

Can you count the number of triangles in the given figure?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

A non-stop marathon is the shared favourite sport of three brothers.

*The oldest one is fat and short and trudges slowly on.
*The middle brother's tall and slim and keeps a steady pace.
*The youngest runs just like the wind, speeding through the race.

"He is young in years, we let him run!" the other two brothers explained, "'because though he is surely number one, he is second, in a way." Why is it?

f you were running a race, and you passed the person in 2nd place, what place would you be in now?

If a boy blows 18 bubbles,
Then pops 6 eats 7 and then
He pops 5 and blows 1.
How many are left?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?