# Thread: Inverse and Power Matrices

1. ## Inverse and Power Matrices

I have a simple 2 x 2 matrix, a =

-1 2
1 3

Correct me if I'm wrong, but the inverse of this matrix is:

1/5 -2/5
-1/5 -3/5

How would I take a^3? Would it be:

-1^3 2^3
1^3 3^3

What would (A^-1)^3 be?

2. First calculate $\displaystyle A^2= A.A$ then find $\displaystyle A^3$ after.

$\displaystyle A^3$ will be $\displaystyle =A^2.A$

3. Originally Posted by aaronrj
I have a simple 2 x 2 matrix, a =

-1 2
1 3

Correct me if I'm wrong, but the inverse of this matrix is:

1/5 -2/5
-1/5 -3/5
Yes, you are wrong. It should be fairly easy to see that, multiplying the first row of the first matrix by the first column of the second, (-1)(1/5)+ 2(-1/5)= -3/5 when it should be 1. It looks like you have just divided the numbers in the matrix by the determinant. That does NOT give the inverse matrix.

How would I take a^3? Would it be:

-1^3 2^3
1^3 3^3

What would (A^-1)^3 be?
It looks like either you do not know how to multiply matrices or you simply have not thought about multiplying matrices in connection with either of these problems. What is A multiplied by itself?