# Thread: Prove that W is symmetric

1. ## Prove that W is symmetric

I know that:

W = W transpose

is symmetric,

but how would I go about this question, how would I get started?

Any help is appreciated!

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.