How to name a square matrix with zeros/ones entries?

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I would like to know is there exist the term for a square matrix like this: $$A=\left(\begin{array}{ccccc} 0&0&0&0&1\\ 0&0&0&0&1\\ 0&0&0&0&1\\ 0&0&0&0&1\\ 0&0&0&0&1 \end{array}\right). $$ All entries of the matrix $A$ are zero with the exception of the last column where all entries equal are to the unit. Is it possible to write the matrix $A$ more shortly for any size?