Provide an appropriate response.
-Suppose that A and 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 $r 1$
C) If $r = s$
D) There are no conditions under which both products can be found.

Question

Provide an appropriate response.
-Suppose that A and 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 $r > 1$
C) If $r = s$
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 match the number of rows in the second matrix. Since both A and B are of dimension $r \times s$, for both AB and BA to be defined, it means that A and B must be square matrices of the same size, hence $r = s$.

Provide an Appropriate Response r×s\mathrm { r } \times \mathrm { s }r×s

Provide an Appropriate Response $\mathrm { r } \times \mathrm { s }$