I'm having trouble calculating the condition number of a matrix. I'm trying to get ahead of my class material. Any help would be appreciated.
Question: Calculate the condition number $$k(A) = \|A\|_F \times \|A^{-1}\|_F,$$ for the matrix $$A=\begin{bmatrix} 5 & 6 & 2 \\ 0 & 4 & 1 \\ 0 & 0 & 3\end{bmatrix}.$$ Recall that $\|A\|_F = \sqrt{ \operatorname{Tr}(AA^*)^{\vphantom{l}}}.$
I'm not too sure where to start I've found post that say I must calculate the transpose matrix along with the inverse, but others just take the max row or column inverse and multiply it by the max row or column of the original matrix. Thank you in advance