diagonalizing a matrix;

Let the matrix A =−1 0 00 0 01 0 1.(a) (5 pts) Why is A diagonalizeable?(b) (12 pts) Diagonalize A and find the invertible matrix P by which you diagonalized A.2

Diagonalize the matrix matA={[2 0 0],[1 4 -1],[-2 -4 4]}

What is the main diagonal of a matrix?a.The elements from the top left to the bottom rightb.The elements from the edges to the middlec.The elements from the middle to the edgesd.The elements from the top right to the bottom left

The matrix A𝐴 has eigenvalues −5−5, −1−1, and 22 with corresponding eigenvectors ⎡⎣⎢07−6⎤⎦⎥[07−6], ⎡⎣⎢−13−1⎤⎦⎥[−13−1] and ⎡⎣⎢−764⎤⎦⎥[−764].  Which of the following is a valid diagonalisation?  Select all that apply.This matrix cannot be diagonalisedA=V−1DV𝐴=𝑉−1𝐷𝑉 with V=𝑉= ⎡⎣⎢07−6−13−1−764⎤⎦⎥[0−1−7736−6−14] and D=𝐷= ⎡⎣⎢−5000−10002⎤⎦⎥[−5000−10002]A=V−1DV𝐴=𝑉−1𝐷𝑉 with V=𝑉= ⎡⎣⎢0−1−7736−6−14⎤⎦⎥[07−6−13−1−764] and D=𝐷= ⎡⎣⎢−5000−10002⎤⎦⎥[−5000−10002]A=VDV−1𝐴=𝑉𝐷𝑉−1 with V=𝑉= ⎡⎣⎢0−1−7736−6−14⎤⎦⎥[07−6−13−1−764] and D=𝐷= ⎡⎣⎢−5000−10002⎤⎦⎥[−5000−10002]A=VDV−1𝐴=𝑉𝐷𝑉−1 with V=𝑉= ⎡⎣⎢07−6−13−1−764⎤⎦⎥[0−1−7736−6−14] and D=𝐷= ⎡⎣⎢−5000−10002⎤⎦⎥

Write a program to obtain a matrix and find the sum of its diagonal elements.Note: Only square matrix.Input format :The input consists of the number of rows and columns separated by a space.The second line of the input is matrix elements.Output format :The output prints the sum of diagonal elements.Refer to the sample input and output for format specifications.Sample test cases :Input 1 :3 31 2 34 5 67 8 9Output 1 :15Input 2 :4 412 23 45 5678 89 98 8765 54 32 2114 25 36 58Output 2 :191