# Thread: Prove that W is symmetric

1. ## Prove that W is symmetric

I know that:

W = W transpose

is symmetric,

2. $(W-I)^T = 2W \ \ (\star)$
Using the property that: $(A \pm B)^T = A^T \pm B^T$
we have that: $W^T - I = 2W \ \Leftrightarrow \ {\color{blue}I = W^T - 2W}$
Now take the transpose of both sides of $(\star)$ and solve for $I$. Compare this expression with what we have in blue and you should get what you want.
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