solve this linear algebra problem

2. a) Consider the following matrix A : A=301412602 Find a basis of R3 consisting of eigenvectors of A. Suppose A is a 3 by 3 matrix with eigenvalues 0,1 and 2 . Identify the following: i. the rank of A ii. the determinant of ATA iii. the determinant of A+I iv. the eigenvalues of (A+I)1