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=[(1,1),(0,1)]` and P is a orthogonal martix and `B=PAP^T, P^TB^2009 P=` (A) `[(1,2009),(0,1)]` (B) `[(1,2009),(2009,1)]` (C) `[(1,0),(2009,1)]` (D) `[(1,0),(0,1)]`

A square matrix A is said to be orthogonal if A^T A=I If A is a square 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 above information answer the following question: IF A is a 3xx3 orthogonal matrix such that |A|=1, then |A-I|= (A) 1 (B) -1 (C) 0 (D) none of these

A square matrix A is said to be orthogonal if A^T A=I If A is a square 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 and B of same order \|AB|=|A||B| On the basis of above information answer the following question: If A=[(p,q,r),(q,r,p),(r,p,q)] be an orthogonal matrix and pqr=1, then p^3+q^3+r^3 may be equal to (A) 2 (B) 1 (C) 3 (D) -1

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 matrix and k is a scalar; then (kA)^(T)=k(A^(T))

If A is square matrix of order 3,|A|=1000 and |kA^(-1)|=27, then k is

A square matrix B is said to be an orthogonal matrix of order n if BB^(T)=I_(n) if n^(th) order square matrix A is orthogonal, then |adj(adjA)| is

If A is a square matrix of order n xx n and k is a scalar, then adj (kA) is equal to (1) k adj A (2) k^n adj A (3) k^(n-1) adj A (4) k^(n+1) adj A

If A is a skew symmetric matrix of order n and C is a column matrix of order nxx1 , then C^(T)AC is

If A=[(3,-4),(-1,2)] and B is a square matrix of order 2 such that AB=I then B=?