Matrix question please help! A^2?

Question

A=
0 1
-1 1
Calculate A^2=

A^3=

A^1660=

0 -1
1 1

Answer 1

Let's do your original matrix A first. Then you
can do the other one by the same method.
0 1
-1 1
squared is
- 1 1
-1 0
Do you see how to get this? To get element p_i,j
of the product AB simply take the dot product
of row i of A with column j of B.
Now, carrying this one step further,
A³ =
-1 0
0 -1
or A³ = -I
So A^4 = -A
A^5 = -A²
and A^6 = I.
So the cycle of products repeats every 6th power.
and we get
A^1660 = A^(6*276 + 4) = A^4 =
0 -1
1 -1

Now you work out the second example!

Answer 2

movie? i thought she meant Toyota Matrix.

Answer 3

Oh, I thought you meant the movie.