The Frobenius norm of a matrix AAA is defined as ∥A∥F=∑i,jaij2\|A\|_F = \sqrt{\sum_{i,j} a_{ij}^2}∥A∥F=∑i,jaij2. What is ∥A∥F\|A\|_F∥A∥F for A=(1234)A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}A=(1324)?
10\sqrt{10}10
30\sqrt{30}30
20\sqrt{20}20
101010