Finding the square root of a matrix

[smerhej]

Homework Statement

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.

Homework Equations

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

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 XD^1/2X^-1 will give me that, so would I just multiply X by D^1/2 , and then by X^-1? I tried that, and it gave me A=

-1 -1
6 4​

 

[I like Serena]

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

 

[smerhej]

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

 

[I like Serena]