Consider the following sets:
V₁ = {(A | A ∈ M₂ ₓ ₂ (R) and A is a symmetric matrix, i.e., A = Aᵀ}
V₂ = {(A | A ∈ M₂ ₓ ₂ (R) and A is a scalar matrix}
V₃ = {(A | A ∈ M₂ ₓ ₂ (R) and A is a diagonal matrix}
V₄ = {(A | A ∈ M₂ ₓ ₂ (R) and A is a upper triangular matrix}
V₅ = {(A | A ∈ M₂ ₓ ₂ (R) and A is a lower triangular matrix}
Chose the set of correct options.
a. Only V₁ is a subspace of M₂ ₓ ₂ (R)
b. Only V₄ is a subspace of M₂ ₓ ₂ (R)
c. Both V₂ and V₃ are subspace of M₂ ₓ ₂ (R)
d. All are subspace of M₂ ₓ ₂ (R)