Assuming matrix $B$ is symmetric, can I prove that $A$ is symmetric $A,B$ are square matrices and $A(I+B)=I$, $B$ is symmetric, can I prove that $A$ is symmetric as well?

Given $B$ is symmetric.
$A(I+B) = I =(I+B)^T \times A^T = (I+B) A^T$
$$A(I+B)A^T = A = IA^T =A^T$$ so $A$ is symmetric!
