Provide an appropriate response.
-Suppose that $\mathrm { A }$ and $\mathrm { B }$ are both matrices of dimension $\mathrm { r } \times \mathrm { s }$. Under what conditions can both the product $\mathrm { AB }$ and the product $\mathrm { BA }$ be found?
A) If $r = 1$
B) If $r = s$
C) If $r 1$
D) There are no conditions under which both products can be found.

Question

Provide an appropriate response.
-Suppose that $\mathrm { A }$ and $\mathrm { B }$ are both matrices of dimension $\mathrm { r } \times \mathrm { s }$. Under what conditions can both the product $\mathrm { AB }$ and the product $\mathrm { BA }$ be found?
A) If $r = 1$
B) If $r = s$
C) If $r > 1$
D) There are no conditions under which both products can be found.

Quizplus · Accepted Answer

For matrix multiplication to be possible, the number of columns in the first matrix must equal the number of rows in the second matrix. Therefore, for both AB and BA to exist, A and B must be square matrices of the same dimension, implying $r = s$.

Provide an Appropriate Response A\mathrm { A }A And B\mathrm { B }B

Provide an Appropriate Response $\mathrm { A }$ And $\mathrm { B }$