Please prove the following laws

a.(bxc)= b.(cxa)=c.(bxa)

ax(bxc)=b(a.c) -c(a.b)

(axb).(cxd)= (a.c)(b.d) -(a.d)(b.c)

ax(bxc) +bx(cxa) + cx(axb) = 0

(axb)x(cxd) = b(a.(cxd))-a.(b.(cxd))

= c(a.(bxd)) - d(a.(bxc)

(axb).((bxc)x(cxa))= (a.(bxc))^2

thank you!