If P and Q are two non-singular matrices such that `PQ = QP,` then `(P(P + Q)^-1 Q)^-1(PQ)` is

If P and Q are symmetric matrices of the same order then PQ- QP is

If P and Q are symmetric matrices of the same order then PQ-QP is

If P and Q are symmetric matrices and PQ=QP then which of the following is/are true (A) QP^-1=P^-1Q (B) PQ is skew symmetric (C) P^-1Q is symmetric (D) both (a) and (c)

If P and Q are symmetric matrices and PQ=QP then which of the following is/are true (A) QP^(-1)=P^(-1)Q(B)PQ is skew symmetric (C) P^(-1)Q is symmetric (D) both (a) and (c)

Let P and Q be two 2xx2 matrices. Consider the statements (i) PQ=OimpliesO or Q=O or both (ii) PQ=I_(2)impliesP=Q^(-1) (iii) (P+Q)^(2)=P^(2)+2PQ+Q^(2) . Then

If p and q are distinct integers such that 2005 + p = q^2 and 2005 + q = p^2 then the product p.q is.

If P^2 + 4 Q^2 = 4PQ , then determine P : Q

Find the inverse of each of the matrices given below : Obtain the inverse of the matrics [(1,p,0),(0,1,p),(0,0,1)] and [(1,0,0),(q,1,0),(0,q,1)] . And, hence find the inverse of the matrix [((1+pq),p,0),(q,(1+pq),p),(0,q,1)] . Let the first two matrices be A and B. Then, the third matrix is AB. Now, (AB)^(-1)=(B^(-1)A^(-1))

If p + q = 6 and pq = 8 , then p^(3) + q^(3) is equal to

Two forces P and Q are in ratio P:Q=1:2 . If their resultant is at an angle tan^(-1)((sqrt3)/(2)) to vector P, then angle between P and Q is :