Express the following matrix as a sum of a symmetric and skew-symmetric matrix
`[(3,3,-1),(-2,-2, 1),(-4,-5,2)]`

Express the matrix A as the sum of a symmetric matrix and a skew-symmetric matrix, where A=[(2,4,-6),(7,3,5),(1,-2,4)]

Prove that a matrix which is symmetric as well as skew-symmetric is a null matrix.

Express [(2,3,4),(5,6,-2),(1,4,5)] as the sum of a symmetric matrix and a skew-symmetric matrix.

Prove tha tany square matrix can be expressed uniquely as the sum of a symmetric and a skew-symmetric matrix.

Find the inverse of the matrix A, if A=[(3,-2,3),(2,1,-1),(4,-3,2)]

Express the following in index form : log_4 (1/8)=-3/2

Prove that the diagonal elements of a skew-symmetric matrix are all zero

State whether each of the following binary relations on the set A={1, 2, 3} is reflexive, symmetric and transitive R={(1,1),(2,2),(1,2),(2,1)}

State whether each of the following binary relations on the set A={1, 2, 3} is reflexive, symmetric and transitive R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}

State whether each of the following binary relations on the set A={1, 2, 3} is reflexive, symmetric and transitive R={(1,1),(1,2),(2,3)}