If A and B are two matrices such that A + B and AB are both defin… - Vidyadip

MCQ

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
✓
$A, B$ are square matrices of the same order
D
Number of columns of $A =$ Number of rows of $B$

✓

Answer

Correct option: 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

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