In the answer key they have mentioend that (a), (b) and © are correct, can you please explain how (b) is correct and (d) is not?

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A $n\times n$ matrix $A$ is said to be $symmetric$ if $A^T=A$. Suppose $A$ is an arbitrary $2\times 2$ matrix. Then which of the following matrices are symmetric (here $0$ denotes the $2\times 2$ matrix consisting of zeros):

- $A^TA$
- $\begin{bmatrix} 0&A^T \\ A & 0 \end{bmatrix}$
- $AA^T$
- $\begin{bmatrix} A & 0 \\ 0 & A^T \end{bmatrix}$