A matrix A is skew symmetric if A^T=-A. If A is a skew symmetric matrix, what type of matrix is A^T?

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Well, let's go ahead and rename our matrix $A^T$ so that we can think about it a little easier maybe? Let's call it B.

$$A^T=B$$

Now to see if B is skew symmetric or not, let's plug this into the equation that all skew symmetric matrices must satisfy. If we end up with a true statement then we have shown that it is indeed skew symmetric:

$$B^T=-B$$

Now we can plug in B again now that we're not distracted, and follow through with the algebra:

$$(A^T)^T = -A^T$$

Now we know that the transpose of the transpose of a matrix just undoes it, so the left side's transposes cancel leaving us with just A there. 
$$A = -A^T$$

What about the right side? Well remember they said $A^T=-A$ so we can replace it:

$$A=-(-A)$$

So we see that we get a true statement, therefore if $A$ is skew symmetric so is $A^T$!