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

You are mixing a mixture of cement and Sand with five gallons of water. You have a garden hose giving you all the water you need. The problem is that you only have a four-gallon bucket and a seven-gallon bucket and neither has graduation marks. Find a method to measure five gallons.

Can You Find The Poor LOST PUPPY Hidden In The Park in 20 Seconds?

How can you tell a raw egg from a hard-boiled egg?

An ant is travelling on a 1-meter-long rope at 1 cm/second but also the entire rope is being stretched by an extra 1 meter/second. Is it possible for the ant to reach at the end of the rope?

What's the only room from which no one can enter or leave

Find the next number in the series.
1 10 24 43 67 ?

What is the word or phrase?

A seven-year-old kid challenged his classmates that he can make the number one disappear by adding something to it.

How can he do that?

You measure my life in hours
I serve you by expiring
I vanish faster when I am thin
and slower when I am thick
The wind is my energy
What am I?