Is a Real Number Sufficient for Scalar Multiplication in a Complex Subspace?

[dylanhouse]

Homework Statement

Given W={A belonging to M₂(ℂ) | A is symmetric} is a subspace of M₂(ℂ) over ℂ, when showing it is closed under scalar multiplication, do I need to use a complex scalar as it is over the complex numbers, or will a real number be okay?

Homework Equations

The Attempt at a Solution

 

[kostas230]

You have to prove that it's closed under scalar multiplication using complex numbers, as the vector space $M_2(\mathbb{C})$ is a vector space over the complex numbers.