Find all 2 x 2 matrices such that .

Is there a systematic way to do this?

:confused:

Printable View

- Jul 2nd 2007, 06:47 AMDivideBy0List Matrices
Find all 2 x 2 matrices such that .

Is there a systematic way to do this?

:confused: - Jul 2nd 2007, 07:23 AMred_dog
Let

.

Then .

So .

I. If or

or .

II. If , so that - Jul 2nd 2007, 09:38 AMPlato
This is a rather more straightforward way.

If then

That means that if .

Thus ; that any two-by-two matrix with determinant equal –1 and a=-d has the property. - Jul 2nd 2007, 10:17 PMDivideBy0
But doesn't exclude the possibility of the

[1 0]

[0 1]

matrix? or the

[-1 0]

[0 -1]

or are they just exceptions? - Jul 3rd 2007, 02:37 AMtopsquark