Choose the wrong statement.

For every matrix A, AA' + A'A is defined

The correct answer is Option (3) → For every matrix A, AA' + A'A is defined

Let matrix $A$ be of order $m \times n$.

• $AA'$ will be of order $m \times m$
• $A'A$ will be of order $n \times n$

For addition, matrices must have the same order. Since $m \neq n$ in general, $AA' + A'A$ is not always defined.

Hence, Option (3) is incorrect.

• Option (1): True $\to$ $AA'$ and $A'A$ are always square
• Option (2): True $\to$ $AA'$ is always symmetric
• Option (4): True $\to$ If $A$ is square ($n \times n$), both are same order, so addition is defined