let n be Nat; :: thesis: for R being Ring
for M1 being Matrix of n,R holds M1 commutes_with 1. (R,n)
let R be Ring; :: thesis: for M1 being Matrix of n,R holds M1 commutes_with 1. (R,n)
let M1 be Matrix of n,R; :: thesis: M1 commutes_with 1. (R,n)
( M1 = M1 * (1. (R,n)) & M1 = (1. (R,n)) * M1 ) by MATRIX_3:18, MATRIX_3:19;
hence M1 commutes_with 1. (R,n) ; :: thesis: verum