Why is the following set a subspace of $\displaystyle M_{n \times n}^R, n \geq 2$

$\displaystyle B = \{A \in M_{n \times n}^C | A_\downarrow_1 = (1-2i)A_\downarrow_2 \}$

I immediately said it is not a subspace since complex numbers aren't in real numbers. It's the other way around. But I am wrong apparently...