Provide an Appropriate Response $A$ And $B$ Are Two Matrices Such That $A + B , A - B$

Multiple Choice

Provide an appropriate response.
-Suppose that $A$ and $B$ are two matrices such that $A + B , A - B$ , and $A B$ all exist. What can you conclude about the dimensions of $\mathrm { A }$ and $\mathrm { B }$ ?

A) $A$ and $B$ have the same dimension but are not necessarily square matrices.
B) There are no dimensions of $A$ and $B$ that would make this possible.
C) $A$ is a row matrix, and $B$ is a column matrix.
D) $A$ and $B$ are square matrices of the same dimension.