ok, so i know this math problem should be easy, but i really dont understand it. pls help me out!

the following are supposed to be matrices but i do not know how to make them on the computer.

Let X= (1 1

1 1)

Let Y= (1 -1

-1 1)

Calculate X^2, X^3, X^4, Y^2, Y^3, Y^4

By considering integer powers of X and Y, find expressions for Z^n, Y^n, (X+Y)^n

Let A= aX and B=bY where a and b are constants

Use different values of a and b to calculate A^2, A^3, A^4, B^2, B^3, B^4

By considering interger powers of A and B, find expressions for A^n, B^n, (A+B)^n

Now consider M= (a+b a-b

a-b a+b)

Show that M= A+B and that M^2= A^2+B^2

Hence, find the general statement that expresses M^n in terms of aX and bY

Test the validity of your general statement by using different Values of a, b, n

Discuss the scope and limitations of your general statement

Use an algebraic method to explain how you arrived at your general statement.

Thanks so mcuh for your help!