please help me solving this questions using linear algebra

. (5 points) Let A be a real matrix with characteristic polynomial p()\\) = A2(A+2)3()\\ 5). (a) List the eigenvalues of A in a table, along with their algebraic multiplicities. Use this information to determine the order of the matrix A. (b) Using the fact that tr(A =:a.A- a1A1 + 02A; + + (In/\\m where A1; represents the it" eigenvalue of A and (2.- is it s multiplicity (so the trace of A is the sum of its eigenvalues, counting multiplicity), c0mpute the trace tr(A) of the matrix A. (c) Using the fact that det(A =A'5": A'fl - X\" - - - 1:", where A? is the it\" eigenvalue of A raised to it s multiplicity (so the determinant of A 1s the product of its eigenvalues counting multiplicity) compute the determinant det(A) of A