let n be Nat; :: thesis: for K being Ring
for M1 being Matrix of n,K st M1 is Orthogonal holds
(M1 @) * M1 = M1 * (M1 @)
let K be Ring; :: thesis: for M1 being Matrix of n,K st M1 is Orthogonal holds
(M1 @) * M1 = M1 * (M1 @)
let M1 be Matrix of n,K; :: thesis: ( M1 is Orthogonal implies (M1 @) * M1 = M1 * (M1 @) )
assume A1: M1 is Orthogonal ; :: thesis: (M1 @) * M1 = M1 * (M1 @)
then (M1 @) * M1 = 1. (K,n) by Th43;
hence (M1 @) * M1 = M1 * (M1 @) by A1, Th42; :: thesis: verum