Prove Vector Equations: AB=Im & m<=n

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Homework Statement


A is a mxn matrix and B is a nxm matrix. AB = Im.
a) Prove that there's only one solution to Bx = 0 where x and 0 are coloum vectors.
b) Prove that m<=n


Homework Equations


if A is a mxn n>m then there're infinite solutions to Ax=0


The Attempt at a Solution


a) Bx=0 => ABx=A0 => Ix=0 => x=0 so there's only the trivial solution.
b) according to the equation above if m>n then there would be an infinite amount of solutions to Bx=0 and not only one.
Did I do that right? This was a problem on an exam and it relative to the other questions it looks to easy.
 
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Hm, looks okay.
 

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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