let n be Nat; :: thesis: for K being Field
for M1, M2 being Matrix of n,K st M1 is Orthogonal & M1 commutes_with M2 holds
M1 @ commutes_with M2
let K be Field; :: thesis: for M1, M2 being Matrix of n,K st M1 is Orthogonal & M1 commutes_with M2 holds
M1 @ commutes_with M2
let M1, M2 be Matrix of n,K; :: thesis: ( M1 is Orthogonal & M1 commutes_with M2 implies M1 @ commutes_with M2 )
assume A1: ( M1 is Orthogonal & M1 commutes_with M2 ) ; :: thesis: M1 @ commutes_with M2
then ( M1 @ = M1 ~ & M1 is invertible ) by Def7;
hence M1 @ commutes_with M2 by A1, Th41; :: thesis: verum