In my lecture notes, there is this explanation of how to find eigenvalues. There is a step that I don't understand, highlighted in yellow.
Is this a rule of matrix algebra? To me it looks like the notation indicates that you can take the last element (a33) of a 3x3 matrix and put it outside the matrix if a13 = a23 = a31 = a32 = 0. Ie.
\begin{bmatrix}a11&a12&a0\\a21&a22&a0\\0&0&a33\end{bmatrix} Is equal to \begin{bmatrix}a11&a12\\a21&a22\end{bmatrix} Times a33 (Sorry, didn't get the a33 to align nicely with the matrix).
If it is a rule, I would appreciate knowing what it is called so I can read about it. If it is not a rule, I would appreciate an explanation of what is being done in this procedure.