Suppose that we have the following four matrices

(a) Which pairs of matrices can be validly multiplied together?
For these pairs, perform the multiplications.

(b) Calculate 2A, 3B,

(c) Calculate Tr(A), Tr(B), Tr(A + B) and verify that Tr(A) +
Tr(B) = Tr(A + B)

(d) What is the rank of the matrix A?

(e) Find the eigenvalues of the matrix (A + B)

(f) What will be the trace of the identity matrix of order 12?