Multiplying row exchange matrices

Arnoldjavs3
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Homework Statement


Multiply these row excahnge matrices in the order pq qp and p^2
p =
[0 1 0]
[1 0 0]
[0 0 1]

q=
[0 0 1]
[0 1 0]
[1 0 0]

Homework Equations

The Attempt at a Solution


I don't understand why the solution is
[0 1 0]
[0 0 1]
[1 0 0]

do you not multiply rows by columns? When i do this i just get a 3x3 with 0s in the entire matrix. I don't understand, what am I doing wrong? Since this is a fundamental misunderstanding from my part.
 
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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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