Question

If $A$ and $B$ are two matrices such that $A+B$ and $AB$ are both defined, then

• A. $A$ and $B$ can be any matrices
• B. $A$, $B$ are square matrices not necessarily of the same order
• C. $A,B$ are square matrices of the same order
• D. number of columns of $A=$ number of rows of $B$

Answer 1

The correct option is C $A,B$ are square matrices of the same order

Let $A$ and $B$ both have a matrices of order $m\times n$
Also $AB$ is defined, it means $m=n$
Hence $A$ and $B$ are square matrices of same order