Determinant of matrix order >=4

Introduction |Order of determinant|Determinant of Matrix |Properties of Determinant |Previous year questions |Area of a Triangle

Introduction |Order of determinant|Determinant of Matrix |Properties of Determinant |Previous year questions |Area of a Triangle

Statement -1 : Determinant of a skew-symmetric matrix of order 3 is zero. Statement -2 : For any matrix A, Det (A) = "Det"(A^(T)) and "Det" (-A) = - "Det" (A) where Det (B) denotes the determinant of matrix B. Then,

If A is matrix of order 3 such that |A|=5 and B= adj A, then the value of ||A^(-1)|(AB)^(T)| is equal to (where |A| denotes determinant of matrix A. A^(T) denotes transpose of matrix A, A^(-1) denotes inverse of matrix A. adj A denotes adjoint of matrix A)

Statement 1: The determinant of a matrix A=[a_(ij)]_(5xx5) where a_(ij)+a_(ji)=0 for all i and j is zero.Statement 2: The determinant of a skew-symmetric matrix of odd order is zero

If D is the determinant of a square matrix A of order n, then the determinant of its adjoint is

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.

Find the determinant of a matrix [{:(2,-3),(4," "5):}]