There is an invertible matrix P for which is a diagonal matrix. If P exists then A is diagonalizable. Do you know how to find P? Have you learnt about diagonalizability? Your 3x3 matrix A is diagonalizable if A has 3 linearly independent eigenvectors. So, the first step you have to find eigenvectors of A, say . Then form the matrix . the matrix will be diagonal and upper triangular and will have the eigenvalues corresponding to , respectively, as its successive diagonal entries. Let's see how you go.