Show that, for the space of all m × n {\displaystyle {}m\times n} -matrices Mat m × n ( K ) {\displaystyle {}\operatorname {Mat} _{m\times n}(K)} , the matrices E i j {\displaystyle {}E_{ij}} that have in position ( i , j ) {\displaystyle {}(i,j)} the entry 1 {\displaystyle {}1} , and elsewhere 0 {\displaystyle {}0} , form a basis.
