Prove that if matrix A is diagonalizable with in real eigenvalues A, A2, There exists an invertible matrix P and a diagonal matrix D, such that O Determinant of a Matrix Product Definition of the Inverse of a Matrix Properties of the Identity Matrix Determinant of a Triangular Matrix Determinant of an Inverse Matrix Definition of a Diagonalizable Matrix Eigenvalues of Triangular Matrices Associative Property of Matrix Multiplication Similar Matrices Have the Same Eigenvalues The eigenvalues of D are A, A, Determinant of a Matrix Product Definition of the Inverse of a Matrix Properties of the Identity Matrix Determinant of a Triangular Matrix Determinant of an Inverse Matrix Definition of a Diagonalizable Matrix Eigenvalues of Triangular Matrices Associative Property of Matrix Multiplication Similar Matrices Have the Same Eigenvalues The diagonal elements of D are A, A, A Determinant of a Matrix Product Definition of the Inverse of a Matrix Properties of the Identity Matrix Determinant of a Triangular Matrix O Determinant of an Inverse Matrix Definition of a Diagonalizable Matrix Eigenvalues of Triangular Matrices Athen |A|AAA. Complete the proof by justifying each step. P-1AP= D. |A| = |IAI Determinant of a Matrix Product Definition of the Inverse of a Matrix Properties of the Identity Matrix Determinant of a Triangular Matrix Determinant of an Inverse Matrix Definition of a Diagonalizable Matrix Eigenvalues of Triangular Matrices Associative Property of Matrix Multiplication Similar Matrices Have the Same Eigenvalues |A| = |(PP-1)A(PP-1)| Determinant of a Matrix Product Definition of the Inverse of a Matrix Properties of the Identity Matrix O Determinant of a Triangular Matrix Determinant of an Inverse Matrix Definition of a Diagonalizable Matrix Eigenvalues of Triangular Matrices Associative Property of Matrix Multiplication Similar Matrices Have the Same Eigenvalues |A| = |P(P-AP) P-1| = |PDP-11 Determinant of a Matrix Product Definition of the Inverse of a Matrix Properties of the Identity Matrix Determinant of a Triangular Matrix O Determinant of an Inverse Matrix Definition of a Diagonalizable Matrix Eigenvalues of Triangular Matrices Associative Property of Matrix Multiplication |A| = |P||D||P-1 Determinant of a Matrix Product Definition of the Inverse of a Matrix Properties of the Identity Matrix Determinant of a Triangular Matrix Determinant of an Inverse Matrix Definition of a Diagonalizable Matrix Eigenvalues of Triangular Matrices Associative Property of Matrix Multiplication Similar Matrices Have the Same Eigenvalues |A| = |P||0| = 101 Determinant of a Matrix Product Definition of the Inverse of a Matrix Properties of the Identity Matrix Determinant of a Triangular Matrix O Determinant of an Inverse Matrix Definition of a Diagonalizable Matrix Eigenvalues of Triangular Matrices Associative Property of Matrix Multiplication Similar Matrices Have the Same Eigenvalues |A|dd.dn O Determinant of a Matrix Product Definition of the Inverse of a Matrix Properties of the Identity Matrix Determinant of a Triangular Matrix Determinant of an Inverse Matrix Definition of a Diagonalizable Matrix Eigenvalues of Triangular Matrices Associative Property of Matrix Multiplication