Diagonalize the matrix `A=[[3,1,-1],[-2,1,2],[0,1,2]]`

(i) Show that the matrix A=[[1,-1, 5],[-1, 2, 1],[ 5, 1, 3]] is a symmetric matrix. (ii) Show that the matrix A=[[0, 1,-1],[-1, 2, 1],[ 1,-1, 0]] is a skew symmetric matrix.

Find the rank of the matrix A = [[0,1,2,-2],[4,0,2,6],[2,1,3,1]]

4.Find the rank of the matrix A = [[4,2,-1,2],[1,-1,2,1],[2,2,-2,0]]

Find the rank of the matrix A = [[1,3,2],[-1,7,2],[1,0,1]]

Find the Rank of the matrix A = [[1,4,5,2],[2,1,3,0],[-1,3,2,2]]

Find the rank of the matrix A = [[1,2,-1,3],[3,-1,2,1],[2,-2,3,2],[1,-1,1,-1]]

For the matrix A=[[1,-1, 1],[ 2 ,3, 0 ],[18 ,2 ,10]] , show that A(a d j\ A)=O .

Using elementary transformations, find the inverse of the matrix [[2, 0,-1],[ 5, 1, 0],[ 0, 1 ,3]]

Find the rank of matrix A= [[1,2,-1,0],[0,1,3,1],[2,5,1,2]]

Find the rank of the matrix [[1,2,3],[3,2,1],[1,3,2],[2,1,3]]