Show that the matrix `A=[[1,-1,5],[-1,2,1],[5,1,3]]` is symmetric.

(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.

(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.

Show that the matrix A=[[1,2,2],[2,1,2],[2,2,1]] satisfies the equation A^2-4A-5I_3=0 and hence find A^(-1)

Show that the matrix A=[[1 ,2, 2],[ 2, 1, 2],[ 2, 2, 1]] satisfies the equation A^2-4A-5I_3=O and hence find A^(-1) .

If the matrix A=[[0,a,-3],[2,0,-1],[b,1,0]] is skew-symmetric, find the values of a ,\ b .

If the matrix A = [[0,a,-3],[2,0,-1],[b,1,0]] is skew symmetric, find the value of a and b .

show that the matrix A=[(-5,-8,0),(3,5,0),(1,2,-1)] is involutory.

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

For what value of x is the matrix A=[(0,1,-2),(1,0,3),(x,3,0)] a skew-symmetric matrix?

For what value of x is the matrix A=[(0,1,-2),(1,0,3),(x,3,0)] a skew-symmetric matrix?