Determine whether the given set s is a subspace of the vector space v.
a. v = m_3 (r) and s is the set of 3 times 3 matrices with trace 0 (recall the trace of a matrix is the sum of its diagonal entries)
b. v = m_3(r) and s is the set of 3 times 3 matrices of rank 1
c. v = m_3 (r) and s is the set of 3 times 3 matrices a such that the vector (7 4 3) is in the of a
d. v = m_2(r) and s is the set of 2 times 2 matrices a such that a^2 = o (here o is the 2 times 2 zero matrix)
e. v = m_2 (r) and s is the set of 2 times 2 matrices that commute with the matrix (0 5 1 6)
f. v = m_3(r) and s is the set of 3 times 3 matrices a such that a^2 = a