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

If A is a square matrix of order n and A A^T = I then find |A|

If A=[a_(ij)] is a scalar matrix of order nxxn and k is a scalar, then abs(kA)=

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 square matrix of order nxxn and lamda is a scalar then |lamdaA| is (A) lamda|A| (B) lamda^n|A| (C) |lamda||A| (D) none of these

The trnsformation orthogonal projection on X-axis is given by the matrix (A) [(0,1),(0,0)] (B) [(0,0),(0,1)] (C) [(0,0),(1,0)] (D) [(1,0),(0,0)]

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 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 square matrix of order 3 such that abs(A)=2, then abs((adjA^(-1))^(-1)) is