Diagonalizable Matrices: Proof of AB being Diagonalizable

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Homework Statement


Prove if A and B are two diagonalizable matrices of the same size, then AB is also diagonalizable.


Homework Equations





The Attempt at a Solution

 
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timberchris said:

Homework Statement


Prove if A and B are two diagonalizable matrices of the same size, then AB is also diagonalizable.


Homework Equations





The Attempt at a Solution


Welcome to Physics Forums!

Being that this is your first post, you probably haven't taken time to look at the rules, which say that you need to make an attempt at a solution before we can help.

What is the definition of a "diagonalizable" matrix? That's pertinent here.
 

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...
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