please answer (b) & Question4(b) and Question (5) .. please do all of these I will give u upvote otherwise not done all I will give downvote

(b) If V,W are of dimension m,n respectively over F, then show that Linm,nMatnmF. UNIT-2 Question 4. (a) State and prove the Cayley Hamilton Theorem. (b) Prove that an nn matrix is diagonalizable if and only if it admits n linearly independent eigenvectors. Question 5. For the matrix A given by 101010101 Find the matrix P such that P1AP is diagonal