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

Show that the matrix A=[(0, 1,-1),(-1,0,1),(1,-1,0)] is a skew symmetric matrix.

show that the matrix A=[(2,-2,-4),(-1,3,4),(1,-2,-3)] is idempotent.

For what value of k the matrix [(2k+3,4,5),(-4,0,-6),(-5,6,-2k-3)] is a skew symmetric matrix ?

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

For the matrix A=[(1,5),(6,7)] , verify that (i) (A+A') is a symmetric matrix (ii) (A-A') is a skew symmetric matrix

find the adjoint of the matrix A=[(1,2,3),(0,5,0),(2,4,3)]

Express the matrix B=[(2,-2,-4),(-1,3,4),(1,-2,-3)] as the sum of a symmetric and a skew symmetric matrix.

The inverse of the matrix [(2,5,0),(0,1,1),(-1,0,3)] is

find the real value of x for which the matrix =[(x+1,3,5),(1,x+3,5),(1,3,x+5)] is non-singular.

The symmetric part of the matrix A=[(1,2,4),(6,8,2),(2,-2,7)] is