Chapter 3, Problem 30P

To determine

(a)

If $A*B=B*A$ using the matrices $A,B$ and $C$ from the problem $29$.

To determine

(b)

If $A\ast \left(B*C\right)=\left(A\ast B\right)\ast C$ using the matrices $A,B$ and $C$ from problem $29$.

To determine

(c)

If ${\left(A\ast B\right)}^{\text{t}}=\left(A^{\text{t}}\ast B^{\text{t}}\right)$ using the matrices $A,B$ and $C$ from problem $29$.

To determine

(d)

If ${\left(A+B\right)}^{\text{t}}=A^{\text{t}}+B^{\text{t}}$ using the matrices $A$ and $B$ from problem $29$.