What does the notation $P_{ij} ([i, j],[i, j])$ mean for matrices?

Question

I am looking at my notes from class. We are given a matrix $A$, and in connection to Givens rotations, I see the notation $P_{ij} ([i, j],[i, j]) = \begin{bmatrix} c & s\\ -s & c \end{bmatrix} $

So I assume it means "the $2 \times 2$ matrix with entry $1, 1$ being entry $a_{ii}$ of $A$, entry $1, 2$ being entry $a_{ij}$ of $A$, etc."

Is this what the notation really means?

Thank you very much.