Orthogonal matrix

Which of the following is incorrect? 1. Determinant of Nilpotent matrix is 0 2. Determinant of an Orthogonal matrix = 1 or -1 3. Determinant of a Skew - symmetric matrix is 0. 4. Determinant of Hermitian matrix is purely real.

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.

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 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

[" 64.Let "A=[[0,-sqrt((2)/(3)),(1)/(sqrt(3))],[(1)/(sqrt(2)),-(1)/(sqrt(6)),-(1)/(sqrt(3))],[(1)/(sqrt(2)),(1)/(sqrt(6)),(1)/(sqrt(3))]]" ,then which one of "],[" the following is correct? "],[" (1) "A" is an involutory matrix "],[" (2) "A" is an idempotent matrix "],[" (3) "A" is an orthogonal matrix "],[" (4) "A" is a singular matrix "]

A square matrix A with elements form the set of real numbers is said to be orthogonal if A' = A^(-1). If A is an orthogonal matris, then

If A is any square matrix such that A+(I)/(2) and A-(I)/(2) are orthogonal matrices,then

The product of two orthogonal matrices is 1-orthogonal 2-involuntry 3-unitary 4-idempotent

A and B are two orthogonal matrices of order 3. then(A) A and B both will be invertible matrices (B) matrix ABA will also be orthogonalmatrix AB- will also be orthogonamaximum value of dead 2B)

If both A-(1)/(2) Iand A+(1)/(2) are orthogonal matices,then (a) A is orthogonal (b) A is skew- symmetric matrix of even order (c)A^(2)=(3)/(4)I (d)none of these