Let `A_i` denote a square matrix of order `n xx n` with every element a; Then, the sum of all elements of the product matrix `(A_1 A_2...A_n)` is

Let A_(r) denote a scalar matrix of order n xx n with each diagonal element as r.Then,the trace of the matrix (A_(1)A_(2)A_(3)...A_(n)), is

Let A be a square matrix of order 3 so that sum of elements of each row is 1 . Then the sum elements of matrix A^(2) is

Let A be a square matrix of order 3 so that sum of elements of each row is 1 . Then the sum elements of matrix A^(2) is

Let A be a square matrix of order 3 so that sum of elements of each row is 1 . Then the sum elements of matrix A^(2) is

Let A be a square matrix of order 3 so that sum of elements of each row is 1 . Then the sum elements of matrix A^(2) is

Consida square matrix A of order 2 which has its elements as 0, 1, 2 and 4. Let N denotes the number of such matrices.

Let A be a square matrix of order n; then the sum of the product of elements of any row (column) with their cofactors is always equal to det A

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

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