Question

If $A$ and $B$ are matrices of order $3\times 2$ and $C$ is of order $2\times 3$, then which of the following matrices is not defined-

• A. $A^T+B$
• B. $A^T+B^T$
• C. $A^T+C$
• D. $B+C^T$

Answer 1

The correct option is A $A^T+B$

Given order of $A$ is $3\times 2$
$\Rightarrow$ order of $A^T$ is $2\times 3$
Also, given order of $B$ is $3\times 2$
$\Rightarrow$ order of $B^T$ is $2\times 3$
Order of $C$ is $2\times 3$
Since, $A^T,B^T,C$ have same order , so addition of any 2 or all three matrices are defined.
$A^T+B$ is not defined as their orders are different.