# Finding the square root of a matrix!

## 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 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

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

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

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