let K be Field; for A1, A2, B1, B2 being Matrix of K holds <*A1,B1*> (#) <*A2,B2*> = <*(A1 * A2),(B1 * B2)*>
let A1, A2, B1, B2 be Matrix of K; <*A1,B1*> (#) <*A2,B2*> = <*(A1 * A2),(B1 * B2)*>
A1:
len <*A2*> = 1
by FINSEQ_1:39;
len <*A1*> = 1
by FINSEQ_1:39;
hence <*A1,B1*> (#) <*A2,B2*> =
(<*A1*> (#) <*A2*>) ^ (<*B1*> (#) <*B2*>)
by A1, Th74
.=
(<*A1*> (#) <*A2*>) ^ <*(B1 * B2)*>
by Th76
.=
<*(A1 * A2),(B1 * B2)*>
by Th76
;
verum