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 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 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. Since both A and B are $r \times s$ matrices, for both AB and BA to be possible, $r$ must equal $s$, making them square matrices.

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

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