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Is every square matrix a symmetric matrix?

Or

Is every square DIAGONAL matrix is a symmetric matrix?

Please tell which statement is true?
in Linear Algebra
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2 Answers

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The second statement is true.Let's take an example:

$\begin{bmatrix} 1&5 \\ 3 &6 \end{bmatrix}$ is a square matrix and its transpose is $\begin{bmatrix} 1 &3 \\5 & 6 \end{bmatrix}$ which is not equal to original matrix.

And transpose of any diagonal matrix, let's say $\begin{bmatrix} 1 &0 &0 \\ 0& 5 &0 \\ 0&0 &8 \end{bmatrix}$ and its transpose is $\begin{bmatrix} 1 &0 &0 \\ 0& 5 &0 \\ 0&0 &8 \end{bmatrix}$

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thank you! makes sense
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Diagonal matrix :- All non-diagonal elements =0

Symmetric Matrix :- Square matrix that's equal to it's Transpose (AT=A)

We call them symmetric because they are symmetric to main diagonal.

So in that way every Diagonal Matrix is Symmetric Matrix.

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thanks!
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