Solution1: Given Let’s simplify.

Solution1: Given
Let’s simplify
Use DeMoivre’s Theorem we get
Hence,
Solution 2:
Simplify further we get
Solution 3: Given
i):
So,
ii):

iii):
We know that if and then
So,
Hence,
iv):
And
So,
Solution 4: Given matrices
So,
And
Solution 5: Given matrix is
The augmented matrix with identity is
Let’s perform elementary operations