Chapter 13.3, Problem 8E

To determine

(a)

Prove or disprove $A\subseteq A^2$.

To determine

(b)

Prove or disprove if A = A² , then $\lambda \in A$.

To determine

(c)

Prove or disprove $A\left(\lambda \right)=A$.

To determine

(d)

Prove or disprove ${\left(A^{*}\right)}^{*}=A^{*}$.

To determine

(e)

Prove or disprove $A^{*}A=A^{*}$.

To determine

(f)

Prove or disprove $\left|A^n\right|={\left|A\right|}^n$.