If `P` is an orthogonal matrix and `Q=P A P^T an dx=P^T Q^1000 P` then `x^(-1)` is , where A is involutary matrix. `A` b. `I` c. `A^(1000)` d. none of these

If A is an orthogonal matrix then A^(-1) equals a. A^T b. A c. A^2 d. none of these

A square matrix A is said to be orthogonal if A^T A=I If A is a sqaure matrix of order n and k is a scalar, then |kA|=K^n |A| Also |A^T|=|A| and for any two square matrix A d B of same order \AB|=|A||B| On the basis of abov einformation answer the following question: If A is an orthogonal matrix then (A) A^T is an orthogonal matrix but A^-1 is not an orthogonal matrix (B) A^T is not an orthogonal mastrix but A^-1 is an orthogonal matrix (C) Neither A^T nor A^-1 is an orthogonal matrix (D) Both A^T and A^-1 are orthogonal matices.

If A is a non-singular matrix such that A A^T=A^T A and B=A^(-1)A^T , the matrix B is a. involuntary b. orthogonal c. idempotent d. none of these

A square matrix P satisfies P^(2)=I-P where I is identity matrix. If P^(n)=5I-8P , then n is

In Figure, If P Q=P T\ a n d\ /_T P S=/_Q P R , prove that \ P R S is isosceles

If the p^(t h) term of an A.P. is q and the q^(t h) term is p , prove that its n^(t h)t e r mi s(p+q-n)dot

If the p^(t h) term of an A.P. is q and the q^(t h) term is p , prove that its n^(t h)t e r mi s(p+q-n)dot

If the pth, qth, rth, and sth terms of an A.P. are in G.P., t hen p-q ,q-r ,r-s are in a. A.P. b. G.P. c. H.P. d. none of these

Show that every square matrix A can be uniquely expressed as P+i Q ,where P and Q are Hermitian matrices.

If (p+q)t h term of a G.P. is a and its (p-q)t h term is b where a ,b in R^+ , then its pth term is (a). sqrt((a^3)/b) (b). sqrt((b^3)/a) (c). sqrt(a b) (d). none of these