Question

is all nXn matrix is of the form matrix[{Ir,0},{0,0}]

Answer 1

sorry, what is your question exactly?

Answer 2

I am asking is every nXn matrix is of the form of a canonical form 1st row {Ir,0} 2nd row-{0,0}. where Ir= identity matrix with dimension r
\[\left[\begin{matrix}Ir & 0 \\ 0 & 0\end{matrix}\right]\]