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 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.

Let A be an orthogonal non-singular matrix of order n, then |A-I_n| is equal to :

Let A be an orthogonal non-singular matrix of order n, then |A-I_n| is equal to :