Show that the matrix `[[1,-15],[-1,2,1],[5,1,3]]` is symmetric.

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

If the maxtrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is a skew symmetric matrix , find the values of a,b,andc.

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.

Show that the matrix A=[{:(2,3),(1,2):}] satisfies the equation A^2-4A+I=O , where I is 2xx2 identity matrix and O is 2xx2 zero matrix. Using this equation find A^(-1)

Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric .

If A is a skew-symmetric matrix of order 2 and B, C are matrices [[1,4],[2,9]],[[9,-4],[-2,1]] respectively, then A^(3) (BC) + A^(5) (B^(2)C^(2)) + A^(7) (B^(3) C^(3)) + ... + A^(2n+1) (B^(n) C^(n)), is

Show that the points (2, 3, 4), (- 1, - 2, 1), (5, 8, 7) are collinear.

Express the matrix A=[{:(3,3,-1),(-2,-2,1),(-4,-5,2):}] as the sum of a symmetric and a skew symmetric matrix .

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

For the matrix A=[{:(1,1,1),(1,2,-3),(2,-1,3):}] Show that A^3-6A^2+5A+11I=O . Hence find A^(-1)