If two's company, and three's a crowd, then whats four and five ?

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 ape is trying to climb on a pole that is 60 feet high. Due to the slippery surface, the ape climbs 3 feet in a minute only to slip back 2 feet.

How much time do you think the monkey will take to reach the top of the pole?

John left on a horse on Thursday , was gone for two days, and came back on Thursday after completing his work. How did that happen?

I have a head like a cat and feet like a cat, but I am not a cat. What am I?

There is a place where if I stand up straight, I will still be considered sideways.

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

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?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

I look at you, you look at me I raise my right, you raise your left. What am I?