Take the standard expression for the magnetic Maxwell stress tensor $\mathbf{T}{ik}$ (in terms of $\mathbf{B}$) and convert it entirely into an expression involving the magnetic field tensor $\mathbf{F}{ij}$.
The process involves two main substitutions, using the identity derived in part (b) and the trace of that identity.
The magnetic part of the Maxwell stress tensor is:
$$ \mathbf{T}_{ik} = \frac{1}{\mu_0} \left( \mathbf{B}_i \mathbf{B}k - \frac{1}{2} \mathbf{B}^2 \delta{ik} \right) $$
The result derived in part (b) is:
$$ \mathbf{F}{ij} \mathbf{F}{jk} = \mathbf{B}^2 \delta_{ik} - \mathbf{B}_i \mathbf{B}_k $$
Solving this for the dyadic term $\mathbf{B}_i \mathbf{B}_k$:
$$ \mathbf{B}i \mathbf{B}k = \mathbf{B}^2 \delta{ik} - \mathbf{F}{ij} \mathbf{F}_{jk} $$
Substitute the expression for $\mathbf{B}_i \mathbf{B}k$ from Step 2 into the $\mathbf{T}{ik}$ equation from Step 1:
$$ \mathbf{T}{ik} = \frac{1}{\mu_0} \left[ (\mathbf{B}^2 \delta{ik} - \mathbf{F}{ij} \mathbf{F}{jk}) - \frac{1}{2} \mathbf{B}^2 \delta_{ik} \right] $$
Combine the terms containing $\mathbf{B}^2 \delta_{ik}$:
$$ \mathbf{T}{ik} = \frac{1}{\mu_0} \left( \left(1 - \frac{1}{2}\right) \mathbf{B}^2 \delta{ik} - \mathbf{F}{ij} \mathbf{F}{jk} \right) $$
$$ \mathbf{T}{ik} = \frac{1}{\mu_0} \left( \frac{1}{2} \mathbf{B}^2 \delta{ik} - \mathbf{F}{ij} \mathbf{F}{jk} \right) $$
To eliminate the last $\mathbf{B}^2$ term, we take the trace (set $i=k$ and sum) of the part (b) result:
$$ \mathbf{F}{ij} \mathbf{F}{ji} = \mathbf{B}^2 \delta_{ii} - \mathbf{B}_i \mathbf{B}_i $$