Question

Prove that the subset D={(A)subset(M22)| tr(A)=0} is a subspace of M22 tr(A) is the trace A matrix A by the trace of a matrix .we mean the sum of the elements in the main diagonal

Answer 1

the trace function has these properties:
\[ \large \text{tr}(A+B)=\text{tr}(A)+\text{tr}(B) \]
\[ \large \text{tr}(\alpha A)=\alpha\cdot\text{tr}(A) \]