Let α and β be real numbers. Consider a 3 × 3 matrix A such that A2 = 3A + αI. If A4 = 21A + βI, then which of the following is correct?

If matrix A = [[1, 0], [-1, 1]], then find An.

If matrix A = [[1, 0], [0, 3]], then find the value of A5.

Given below are two statements, one labeled as Assertion (A) and the other as Reason (R): Assertion (A): A matrix in which the number of rows and columns are equal is called a square matrix. Reason (R): A matrix is called a unit matrix if all diagonal elements are zero and non-diagonal elements are unity. In light of the above statements, choose the correct answer from the options given below: