let n be Nat; :: thesis: for K being Field
for M1 being Matrix of n,K st M1 is Nilpotent & M1 is Idempotent holds
M1 = 0. K,n
let K be Field; :: thesis: for M1 being Matrix of n,K st M1 is Nilpotent & M1 is Idempotent holds
M1 = 0. K,n
let M1 be Matrix of n,K; :: thesis: ( M1 is Nilpotent & M1 is Idempotent implies M1 = 0. K,n )
assume A1: ( M1 is Nilpotent & M1 is Idempotent ) ; :: thesis: M1 = 0. K,n
then M1 * M1 = 0. K,n by Def2;
hence M1 = 0. K,n by A1, Def1; :: thesis: verum