Question

For the sets A = {a,b} and B = {a,b,c}, determine Ax B, BX A, A2 = Ax A and B2 = BxB.

Answer 1

Answer: Hello!

the cross product between sets is defined as:

if A = {a,b,c} and B = {1,2,3)

then

$AxB = \left[\begin{array}{ccc}a\\b\\c\end{array}\right]x\left[\begin{array}{ccc}1&2&3\end{array}\right] =\left[\begin{array}{ccc}a1&a2&a3\\b1&b2&b3\\b1&b2&b3\end{array}\right]$

where the A took the place of the columns, and B for the files.

then if our sets are A = {a,b} and B = {a,b,c)

a) AxB

$AxB = \left[\begin{array}{ccc}aa&ab&ac\\ba&bb&bc\end{array}\right]$

b) BxA

$BxA = \left[\begin{array}{ccc}aa&ab\\ba&bb\\ca&cb\end{array}\right]$

c) AxA

$AxA = \left[\begin{array}{ccc}aa&ab\\ba&bb\end{array}\right]$

d) BxB

$BxB = \left[\begin{array}{ccc}aa&ab&ac\\ba&bb&bc\\ca&cb&cc\end{array}\right]$

Hope it helps, i know that is kinda hard work with this kind of operations, i tried to make a kinda of map in the first part so you can replace the values of A and B and do the multiplications by yourself, if you have troubles don't doubt of asking.