Multiplying 3-by-3 Matrices A & B: ?? = ?^18 and ?? = ?^18

[Mrmatheco]

Multiplying 3-by-3 Matrices A & B: ?? = ?^18 and ?? = ?^18

Let X and Y represent two matrices. (A and B are also two matrices btw. both 3x3)
?? = ?¹⁸ and ?? = ?¹⁸
Does that mean X and Y has to be the same matrix?
Can you multiply a matrix with two different matrices and still get the same product?

 

[Dr.Peterson]

Let X and Y represent two matrices. (A and B are also two matrices btw. both 3x3)
?? = ?¹⁸ and ?? = ?¹⁸
Does that mean X and Y has to be the same matrix?
Can you multiply a matrix with two different matrices and still get the same product?

What thoughts do you have about that?

What happens if A is invertible?

What if it is not?

(It doesn't matter to your question, but what significance does the 18th power have? Is there a reason you included that?)