electromagnetism - The Electromagetic Tensor and Minkowski Metric Sign Convention

I am trying to figure out how to switch between Minkowski metric tensor sign conventions of (+, -, -, -) to (-, +, +, +) for the electromagnetic tensor $F^{\alpha \beta}$. For the convention of (+, -, -, -) I know the contravariant and covarient forms of the electromagnetic tensor are: $$ F^{\alpha \beta} = \begin{bmatrix} 0 & -\frac{E_{x}}{c} & -\frac{E_{y}}{c} & -\frac{E_{z}}{c} \\ \frac{E_{x}}{c} & 0 & -B_{z} & B_{y} \\ \frac{E_{y}}{c} & B_{z} & 0 & -B_{x} \\ \frac{E_{z}}{c} & -B_{y} & B_{x} & 0 \\ \end{bmatrix} $$ and $$ F_{\alpha \beta} = \eta_{\alpha \mu} F^{\mu v} \eta_{v \beta} = \begin{bmatrix} 0 & \frac{E_{x}}{c} & \frac{E_{y}}{c} & \frac{E_{z}}{c} \\ -\frac{E_{x}}{c} & 0 & -B_{z} & B_{y} \\ -\frac{E_{y}}{c} & B_{z} & 0 & -B_{x} \\ -\frac{E_{z}}{c} & -B_{y} & B_{x} & 0 \\ \end{bmatrix}. $$

Now for the convention of (-, +, +, +) are the contravariant and covariant forms of the electromagnetic tensor just switched from above along with signs?:

$$ F^{\alpha \beta}= \begin{bmatrix} 0 & \frac{E_{x}}{c} & \frac{E_{y}}{c} & \frac{E_{z}}{c} \\ -\frac{E_{x}}{c} & 0 & B_{z} & -B_{y} \\ -\frac{E_{y}}{c} & -B_{z} & 0 & B_{x} \\ -\frac{E_{z}}{c} & B_{y} & -B_{x} & 0 \\ \end{bmatrix} $$ and $$ F_{\alpha \beta} = \eta_{\alpha \mu} F^{\mu v} \eta_{v \beta} = \begin{bmatrix} 0 & -\frac{E_{x}}{c} & -\frac{E_{y}}{c} & -\frac{E_{z}}{c} \\ \frac{E_{x}}{c} & 0 & B_{z} & -B_{y} \\ \frac{E_{y}}{c} & -B_{z} & 0 & B_{x} \\ \frac{E_{z}}{c} & B_{y} & -B_{x} & 0 \\ \end{bmatrix}~? $$

Basically, I am trying to figure out how to switch between the two sign conventions.