For any matrix `A`, `(A^T)^T=A`

For any square matrix A,A A^(T) is a

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,

For any matrix A, A-A' is _________ matrix.

For any matrix a show that A+A^(T) is symmetric matrix

If A is a nonsingular matrix such that A A^(T)=A^(T)A and B=A^(-1) A^(T) , then matrix B is

Let A be a square matrix of order 3, A^(T) be the transpose matrix of matrix A and "AA"^(T)=4I . If d=|(2A^(T)+"AA"^(T)+adjA)/(2)|, then the value of 12d is equal to (|A|lt 0)

Let Aa n dB be two nonsinular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following are correct? B^T A B is symmetric matrix if A is symmetric B^T A B is symmetric matrix if B is symmetric B^T A B is skew-symmetric matrix for every matrix A B^T A B is skew-symmetric matrix if A is skew-symmetric

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.

For any square matrix write whether AA^(T) is symmetric or skew-symmetric.

If A is a square matrix, then write the matrix a d j(A^T)-(a d j\ A)^T .