Please give a step-by-step solution! Thank you!

Consider the following rotation matrix R^ab that transforms vectors from frame f_b to f_a R^ab = [0.45457972 -0.34766601 0.82005221 0.43387382 0.89049359 0.137020690 -0.77788868 0.29351236 0.55564350] (a) Convince yourself that this is indeed a rotation matrix. Remark on any discrepancies you notice. (b) Using MATLAB, determine the Euler eigenaxis e and the Euler egenangle phi, from R^ab. Verify your answer by reconstructing the matrix R^ab = R^ab(e, phi) and comparing it with (1). Verify that R^abe = e. (c) Using MATLAB, compute the eigenvalues and eigenvectors of R^ab. Verify that e is the eigenvector that corresponds to the eigenvalue 1. What are the other eigenvalue/eigenvector pairs? (d) Determine the components of the quaternion (q,q4) directly from R^ab. Verify your answer by reconstructing the matrix R^ab = R^ab(q,q4) and comparing it with (1)