let n be Nat; :: thesis: for K being Field
for M1 being Matrix of n,K holds M1 commutes_with 1. K,n
let K be Field; :: thesis: for M1 being Matrix of n,K holds M1 commutes_with 1. K,n
let M1 be Matrix of n,K; :: thesis: M1 commutes_with 1. K,n
( M1 = M1 * (1. K,n) & M1 = (1. K,n) * M1 ) by MATRIX_3:20, MATRIX_3:21;
hence M1 commutes_with 1. K,n by Def1; :: thesis: verum