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_3:18, MATRIX_3:19;
hence M1 commutes_with 1. (K,n) by Def1; :: thesis: verum