# Homework Help: Finding the square root of a matrix!

1. Nov 28, 2011

### smerhej

1. The problem statement, all variables and given/known data

Let A be the matrix:
-5 -3
18 10

Find an invertible matrix X so that XAX-1 is diagonal. Use this to find a square root of the matrix A.

2. Relevant equations

DetA - xI
(A-$\lambda$I)v = 0

3. The attempt at a solution

So, I found DetA- xI, which gave me the eigenvalues 4 and 1. I found the eigenvectors for each value, giving me X =
-1 -1
3 2

Now what confuses me is finding the square root of A. I understand that XD1/2X-1 will give me that, so would I just multiply X by D1/2 , and then by X-1? I tried that, and it gave me A=

-1 -1
6 4

2. Nov 28, 2011

### I like Serena

If you multiply your final matrix by itself, what do you get?

3. Nov 28, 2011

### smerhej

The original matrix A! Thank you! I don't know how I didn't think of that to check my work..

4. Nov 28, 2011