Given a skew symmetric matrix `A = [ (0, a , 1),(-1, b, 1),(-1, c, 0)]`, the value of `(a + b + c)^2` is

Consider a skew - symmetric matrix A=[(a,b),(-b, c)] such that a, b and c are selected from the set S={0, 1, 2, 3,…………12}. If |A| is divisible by 3, then the number of such possible matrices is

If A=[(2, 0,-3),( 4, 3, 1),(-5, 7, 2)] is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is (a) [(2, 2,-4 ),(2, 3, 4),(-4, 4, 2)] (b) [(2, 4,-5),( 0, 3, 7),(-3, 1, 2)] (c) [(4, 4,-8),( 4, 6, 8),(-8, 8, 4)] (d) [(1, 0 ,0 ),(0 ,1 ,0),( 0, 0, 1)]

A is said to be skew-symmetric matrix if A^(T) = a)A b)-A c) A^2 d) A^3

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

(i) 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

If A is a skew- symmetric matrix, then trace of A is: 1.) 1 2.) -1 3.) 0 4.)none of these

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

The determinant of a skew symmetric matrix of odd order is 0 1 - 1 None of these

If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsingular and C=(A+B)^(-1) (A-B) , then prove that (i) C^(T) (A+B) C=A+B (ii) C^(T) (A-B)C=A-B (iii) C^(T)AC=A

If the matrix A=[0a32b-1c10] is skew- symmetric,find the values of a,b and