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 square matrix such that A^(3)=I , then prove that A is non-singular

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

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 non-singular matrix and (A+I)(A-I) = 0 then A+A^(-1)= . . .

If A is a symmetric and B skew symmetric matrix and (A+B) si non-singular 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

A skew symmetric matrix S satisfies the relations S^(2)+1=0 where I is a unit matrix then SS' is equal to

If A is skew symmetric matrix, then I - A is (where I is identity matrix of the order equal to that of A)