Eigenvalues? DO I have the right idea with this problem?

[SMA_01]

Homework Statement

I'm supposed to find all the eigenvalues for this 2x2 matrix:

0 2
3 0

Homework Equations

The Attempt at a Solution

When I tried to do it with no row interchanges, I got the characteristic characteristic equation:
λ²-6=0

So, instead of solving this, I interchanged the rows of my matrix to get:

3 0
0 2
And then my determinant would be negative right? I got λ=2,3...I was wondering if I did this right?

Any help is appreciated, thanks.

 

[Mark44]

Homework Statement

I'm supposed to find all the eigenvalues for this 2x2 matrix:

0 2
3 0

Homework Equations

The Attempt at a Solution

When I tried to do it with no row interchanges, I got the characteristic characteristic equation:
λ²-6=0

Which means that the eigenvalues are ±√6.

So, instead of solving this, I interchanged the rows of my matrix to get:

3 0
0 2
And then my determinant would be negative right? I got λ=2,3...I was wondering if I did this right?

The latter part is wrong.

The determinant you are investigating is
$$\begin{vmatrix}-\lambda & 2 \\ 3 & -\lambda \end{vmatrix}$$

not
$$\begin{vmatrix}0 & 2 \\ 3 & 0 \end{vmatrix}$$