Linear Algebra Similar Matrices Problem

SuperZero
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Homework Statement



Find two 2 × 2 matrices A and B such that AB fails to be similar to
BA. Hint: it can be arranged that AB is zero but BA is not.


Homework Equations



N/A


The Attempt at a Solution



If AB similar to BA, AB = S-1BAS for some S, so AB DNE S-1BAS?
Or maybe det(AB) DNE det(BA)
I'm really not sure how to do this without guess and check, which I also tried and failed at
 
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You aren't paying much attention to the hint. If AB=0 and BA is not zero, then they aren't similar. Look for a example of that.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

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