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

2, 3, 5, 9, 17, _ What is the next number in the sequence?

The two towns are exactly 100 km apart. John leaves City A driving at 30 km/hr and Jacob leaves City B half an hour later driving at 60 km/hr. Who will be closer to City A when they meet?

In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?

Given below is simple addition with a defined pattern pattern:
7 + 7 = 2
8 + 8 = 4
8 + 5 = 1
6 + 9 = 3
10 + 11 = 9

Can you analyze the pattern and find out the answer for:

4 + 9 = ?

What do you answer even though it never asks you questions?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

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?

If all Goats are Sheep and all Sheep are Deers, are all Deers Goats ?