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$$$\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}} \left[\begin{array}{cc}1 & 0\\1 & 1\end{array}\right]$$$
Your Input
Calculate $$$\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}} \left[\begin{array}{cc}1 & 0\\1 & 1\end{array}\right]$$$.
Solution
Multiply each entry of the matrix by the scalar:
$$${\color{DarkMagenta}\left(\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}}\right)}\cdot \left[\begin{array}{cc}1 & 0\\1 & 1\end{array}\right] = \left[\begin{array}{cc}{\color{DarkMagenta}\left(\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}}\right)}\cdot \left(1\right) & {\color{DarkMagenta}\left(\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}}\right)}\cdot \left(0\right)\\{\color{DarkMagenta}\left(\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}}\right)}\cdot \left(1\right) & {\color{DarkMagenta}\left(\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}}\right)}\cdot \left(1\right)\end{array}\right] = \left[\begin{array}{cc}\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}} & 0\\\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}} & \frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}}\end{array}\right]$$$
Answer
$$$\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}} \left[\begin{array}{cc}1 & 0\\1 & 1\end{array}\right] = \left[\begin{array}{cc}\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}} & 0\\\frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}} & \frac{\sqrt{2}}{\sqrt{\sqrt{5} + 3}}\end{array}\right]\approx \left[\begin{array}{cc}0.618033988749895 & 0\\0.618033988749895 & 0.618033988749895\end{array}\right]$$$A