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 network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

In a science lab, a petri dish hosts a healthy colony of yeast for an experiment. Now every minute, all the yeast cells divide into two. At noon, there was just a single cell of yeast and at 1:22, the Petri dish was half full. Can you calculate when the dish will be full of yeast?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

Can you find the largest Three-digit number whose sum is 14 and whose square is less than 5,00,000?

Only one color, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

A boy was locked in a room by some robbers. All that is in the room is a piano, a calendar, and a bed. The room is locked from the outside. What does he eat, drink, and how does he escape and get out?

Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?