Matrix

Let A = [a_(ij)] " be a " 3 xx3 matrix and let A_(1) denote the matrix of the cofactors of elements of matrix A and A_(2) be the matrix of cofactors of elements of matrix A_(1) and so on. If A_(n) denote the matrix of cofactros of elements of matrix A_(n -1) , then |A_(n)| equals

If A=[a_(i j)] is a square matrix of even order such that a_(i j)=i^2-j^2 , then (a) A is a skew-symmetric matrix and |A|=0 (b) A is symmetric matrix and |A| is a square (c) A is symmetric matrix and |A|=0 (d) none of these

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 matrix A=[a_(ij)] is an upper triangular matrix if (A) it is a square matrix with a_(ij)=0 for igtj (B) it is a square with a_(ij)=0 for iltj (C) it is not a square matrix with a_(ij)=0 for igtj (D) if is not a sqare matrix with a_(ij)=0 for iltj

Let A=[(1,1,1),(1,-1,0),(0,1,-1)], A_(1) be a matrix formed by the cofactors of the elements of the matrix A and A_(2) be a matrix formed by the cofactors of the elements of matrix A_(1) . Similarly, If A_(10) be a matrrix formed by the cofactors of the elements of matrix A_(9) , then the value of |A_(10)| is