I have this series of operations. How can I obtain the matrix?
$ K := E_{12}(27) \cdot E_{13}(2) \cdot E_{15}(7) \cdot E_{23}(23) \cdot E_{45}(3) \cdot E_{41}(12) \cdot E_{52}(2). $
I tried to multiply from right to left (starting with the matrix I listed below). But I don't obtain the matrix I need.
I want to check with you if this is right:
$ E_{52}(2)=\left[ \begin{array}{ c c } 1&0&0&0&0 \\ 0&1&0&0&0 \\ 0&0&1&0&0 \\ 0&0&0&1&0\\ 0&2&0&0&1 \end{array} \right] $
Am I right?