By a (natural) logarithm of a matrix B we mean a matrix A such that eA

Question:

By a (natural) logarithm of a matrix B we mean a matrix A such that eA ‰¡ B.
(a) Explain why only nonsingular matrices can have a logarithm.
(b) Comparing Exercises 9.4.6-8, explain why the matrix logarithm is not unique.
(c) Find all real logarithms of the 2 x 2 identity matrix