Do tensor equations hold with all indices up or down?

I am starting with general relativity and the notation is making me suffer.

If we have, for example, the tensorial equation:
begin{equation}
A^{munu} = K^{munu}
end{equation}
Where $A$ and $K$ are two arbitrary rank 2 tensors, does this equation imply the following?
begin{equation}
A_{munu} = K_{munu}
end{equation}
Or even,begin{equation}
A_mu^nu= K_mu^nu
end{equation}
What we have done in the last two equations is raising or lowering indices with the metric. Is this true?