Matrix with 0: Comparing Analog Matrices

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Homework Statement


i have matrix
\begin{bmatrix}0&0&0\\ 0&a&b\\ 0&c&d\end{bmatrix}
is this matrix analog to
\begin{bmatrix}a&b\\ c&d\end{bmatrix}?
 
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What do you mean by "analog"? The first is a 3x3 matrix, and the second is a 2x2 matrix. Properties and operations with matrices depend on their "dimension". So no, you can't replace them.
 
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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