`|A^(-1)| ne |A|^(-1)` , where A is non-singular matrix.

If A is a non - singular matrix then

(Statement1 Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement - 1 If matrix A= [a_(ij)] _(3xx3) , B= [b_(ij)] _(3xx3), where a_(ij) + a_(ji) = 0 and b_(ij) - b_(ji) = 0 then A^(4) B^(5) is non-singular matrix. Statement-2 If A is non-singular matrix, then abs(A) ne 0 .

Suppose A and B be two ono-singular matrices such that AB= BA^(m), B^(n) = I and A^(p) = I , where I is an identity matrix. Which of the following orderd triplet (m, n, p) is false?

Suppose A and B be two ono-singular matrices such that AB= BA^(m), B^(n) = I and A^(p) = I , where I is an identity matrix. If m = 2 and n = 5 then p equals to

(aA)^(-1)=(1)/(a)A^(-1) , where a is any real number and A is a square matrix.

Find the derivative of (1 + 1/x)/(1 - 1/x) , where x is non zero integer .

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.