If `S` is a real skew-symmetric matrix, then prove that `I-S` is non-singular and the matrix `A=(I+S)(I-S)^(-1)` is orthogonal.

If s is a real skew-symmetric matrix, the show that I-S is non-singular and matrix A= (I+S) (I-S) ^(-1) = (I-S) ^(-1) (I+S) is orthogonal.

If A is a skew-symmetric matrix of order 3, then prove that det A=0.

A is a real skew symmetric such that A^(2)+I=0 then

If is a non-singular matrix, then det (A^(1))=

Show that every skew-symmetric matrix of odd order is singular.

If A=[a_(ij)] is a skew-symmetric matrix,then write the value of sum_(i)a_(ii)

If A=[a_(ij)] is a skew-symmetric matrix,then write the value of sum_(i)a_(ij).

If A is a symmetric and B skew symmetric matrix and (A+B) is non-singular and C=(A+B)^(-1)(A-B), then prove that

If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) C^(T) AC equals to

If A is a non singular matrix; then prove that |A^(-1)|=|A|^(-1)