Question about the transpose of identity and hat matrices

Question

So I know that because the hat matrix and identity matrix are both symmetric,

$H^{T}=H$ and $I^{T}=I$, respectively

so would $(I-H)^{T}=(I-H)$? Sorry if the answer is obvious, I am missing a step in a proof and I do not have much background in linear algebra. Thanks for the help.

edit: replaced "idempotent" with "symmetric"

Answer 1

We know that $(A-B)^T = A^T - B^T$. This means $$(I-H)^T = I^T - H^T $$ A Hat matrix is symmetric and so is the identity matrix so $$ (I-H)^T = I - H $$