Step-by-step Solution:

We are given that \( B = -A^{-1}BA \), and we need to find \( (A + B)^2 \).

Start by expanding \( (A + B)^2 \):
\[ (A + B)^2 = A^2 + AB + BA + B^2. \]

Using the given condition \( B = -A^{-1}BA \), multiply both sides by \( A \) on the left:
\[ AB = -BA. \]

Substitute \( AB = -BA \) into the expansion of \( (A + B)^2 \):
\[ (A + B)^2 = A^2 + AB + BA + B^2 = A^2 + (-BA) + BA + B^2. \]

The terms \( -BA + BA \) cancel out, so:
\[ (A + B)^2 = A^2 + B^2. \]

Thus, the final result is:
\[ (A + B)^2 = A^2 + B^2. \]