let n be Nat; :: thesis: for K being Field
for M1 being Matrix of n,K holds Trace (M1 + (- M1)) = 0. K
let K be Field; :: thesis: for M1 being Matrix of n,K holds Trace (M1 + (- M1)) = 0. K
let M1 be Matrix of n,K; :: thesis: Trace (M1 + (- M1)) = 0. K
( len M1 = n & width M1 = n ) by MATRIX_1:25;
then Trace (M1 + (- M1)) = Trace (0. K,n,n) by MATRIX_4:2
.= Trace (0. K,n)
.= 0. K by Th56 ;
hence Trace (M1 + (- M1)) = 0. K ; :: thesis: verum