Relational Algebra : Cross Product of a Relation with Table-Dum & Table-Dee

Question

I am wondering what would be the result of the following operation:

Let $A$ be a relation with $n$ ($n > 0$) attributes and $t$ ($t > 0$) tuples. Let $TableDum$ be a relation with $0$ attributes and $0$ tuples. Let $TableDee$ be a relation with $0$ attributes and $1$ tuples.

What would the result of the following be? ($\times$ being the cross product)

$R_1 = A \times TableDum\\ R_2 = A \times TableDee$

Would $R_1$ be a relation with $n$ attributes or $0$ attributes? Would $R_1$ be a relation with $0$ tuples? Would $R_2$ be a relation with $n$ attributes or $0$ attributes? Would $R_2$ be a relation with $0$ tuples?

Thank you very much in advance.

Answer 1

$$ A = R_1 \times TableDum = A_(empty)\\ A = R_2 \times TableDee = A $$