Matrix Multiplication Properties for 2x2 Matrices

nokia8650
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Where A = a 2*2 matrix, is the following true:

(A^n)(A^m) = (A^m)(A^n)

Thanks in advance
 
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Take a guess. Tell us why it might be true.
 
Well I think it would be true, however I know that matrix multiplication is non-commutative so I wasnt sure.

Thanks
 
Matrix multiplication isn't commutative in general. But this is special. It IS associative. Both sides of that equation have n+m A's. They are just grouped differently.
 

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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