Let M and N be two `3xx3` nonsingular skew-symmetric matrices such that `Mn=NM`. If `P^(T)` denotes the transpose of P, then `M^(2) N^(2) (M^(T)N)^(-1) (MN^(-1))^(T)` is equal to

Let A and B be two non-singular skew symmetric matrices such that AB = BA, then A^(2)B^(2)(A^(T)B)^(-1)(AB^(-1))^(T) is equal to

Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and M^2=N^4 then which of the following are correct.

The value of .^(n)C_(1)+.^(n+1)C_(2)+.^(n+2)C_(3)+"….."+.^(n+m-1)C_(m) is equal to

Let Aa n dB be two nonsingular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following options are correct? (correct option may be more than one) (a) . B^T A B is symmetric matrix (b) . if A is symmetric B^T A B is symmetric matrix (c) . if B is symmetric B^T A B is skew-symmetric matrix for every matrix A (d) . B^T A B is skew-symmetric matrix if A is skew-symmetric

If m, n in R , then the value of I(m,n)=int_(0)^(1) t^(m)(1+t)^(n)dt is -

Factorise : 2(m^(2)+n^(2))^(2)-3mn(m^(2)+n^(2))-2m^(2)n^(2)

Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a n d""P^2Q""=""Q^2P , then determinant of (P^2+""Q^2) is equal to (1) 2 (2) 1 (3) 0 (4) 1

Let X \ a n d \ Y be two arbitrary, 3xx3 , non-zero, skew-symmetric matrices and Z be an arbitrary 3xx3 , non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?

Factroise the following. 14mn^2 (2m-n)

If m, n are positive quantities, prove that ((mn+1)/(m+1))^(m+1)gen^m .