theorem Th58: :: MATGRP_0:46

for R being Ring
for n, i, j being Nat
for r being Element of R
for A being Matrix of n,R holds
( A * ((1. (R,n)) + (r * (canMat (i,j,n,R)))) = ((1. (R,n)) + (r * (canMat (i,j,n,R)))) * A iff A * (r * (canMat (i,j,n,R))) = (r * (canMat (i,j,n,R))) * A )