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

12345 a famous South Indian actor
567 is a path in jumbled form
8 & 10 are same letters
9 is one among the first six alphabets.
WHO AM I?

You have a 12 liters jug full of water. You have two empty 8 liters and 5 liters jug. How can you divide the water into two equal parts using these jugs?

Andrew’s doctor gives him three pills and tells him to take one every half hour. How much time will have passed by the time Andrew’s taken all three pills?

I am an odd number. Take away a letter and I become even. What number am I?

On rolling two dices (six-sided normal dice) together, what is the probability that the first one comes up with a 2 and the second one comes up with a 5?

13 decks of cards have been mixed. What is the minimum number of cards that must be taken out from the above-mixed cards to guarantee at least one 'four of a kind?

If Bihan is 10, Anirudha is 20, and Kim and Seal are both 5, but Rikold is 10, how much is Kenniger by the same trend?

A man in a car saw a Golden Door, Silver Door and a Bronze Door. What door did he open first?

I have branches, but no fruit, trunk or leaves. What am I?