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 Ma n dN be two 3xx3 non singular skew-symmetric matrices such that M N=N Mdot If P^T denote the transpose of P , then M^2N^2(M^T N^(-1))^T is equal to M^2 b. -N^2 c. -M^2 d. M N

If A=[[3,4],[5,1]] , show that A-A^T is a skew symmetric matrix, where A^T denotes the transpose of matrix A

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.

Let Aa n dB be two nonsinular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following are correct? (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

sum_(p=1)^(n) sum_(m=p)^(n) (("n"),("m"))(("m"),("p")) is equal to

If m and n are positive quantites , prove that ((mn+1)/(m+1))^(m+1)ge n^(m)

lim_(n to oo){(1^(m)+2^(m)+3^(m)+...+ n^(m))/(n^(m+1))} equals

Find the value of the products: (3m-2n)(2m-3n)a t\ m=1,\ n=-1

2{(m-n)/(m+n)+1/3((m-n)/(m+n))^(3)+1/5((m-n)/(m+n))^(5) +..} is equals to

If m=root3(125) and n=root3(64) , find the value of m-n-(1)/(m^(2)+mn+n^(2)) .