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

Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

I have Rs.50 and I spend it in the way as below.

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

This is a picture puzzle. You have to guess the name of the movie that can be related to the picture.

What word is identified by the below rebus?

Your Your Your Your Your
Your Your Your Your Your

What is both possible and impossible at the same time?

I got a bee but no honey.
got an eye but am still blind.
got a sea but no water.
got a tea but no coffee.
got a why but no answer.

What Am I?

There are two beautiful yet remote islands in the South Pacific. The Islanders born on one island always tell the truth, and the Islanders from the other island always lie.
You are on one of the islands and meet three Islanders. You ask the first which island they are from in the most appropriate Polynesian tongue, and he indicates that the other two Islanders are from the same island. You ask the second Islander the same question, and he also indicates that the other two Islanders are from the same island.
Can you guess what the third Islander will answer to the same question?

A swan sits at the center of a perfectly circular lake. At an edge of the lake stands a ravenous monster waiting to devour the swan. The monster can not enter the water, but it will run around the circumference of the lake to try to catch the swan as soon as it reaches the shore. The monster moves at 4 times the speed of the swan, and it will always move in the direction along the shore that brings it closer to the swan the quickest. Both the swan and the the monster can change directions in an instant.
The swan knows that if it can reach the lake's shore without the monster right on top of it, it can instantly escape into the surrounding forest.

How can the swan successfully escape?