The sum of the principal diagonal elements of a square matrix is called

If A_(1), A_(2), A_(3)...........A_(20) are 20 skew - symmetric matrices of same order and B=Sigma_(r=1)^(20)2r(A_(r))^((2r+1)) , then the sum of the principal diagonal elements of matrix B is equal to

If A is 2xx2 matrix such that A[{:(" "1),(-1):}]=[{:(-1),(2):}]and A^2[{:(" "1),(-1):}]=[{:(1),(0):}] , then trace of A is (where the trace of the matrix is the sum of all principal diagonal elements of the matrix )

Consider the matrix A=[(x, 2y,z),(2y,z,x),(z,x,2y)] and A A^(T)=9I. If Tr(A) gt0 and xyz=(1)/(6) , then the vlaue of x^(3)+8y^(3)+z^(3) is equal to (where, Tr(A), I and A^(T) denote the trace of matrix A i.e. the sum of all the principal diagonal elements, the identity matrix of the same order of matrix A and the transpose of matrix A respectively)

The number of matrices X with entries {0,2,3} for which the sum of all the principal diagonal elements of X.X^(T) is 28 (where X^(T) is the transpose matrix of X), is

Trace of a scalar matrix of order 4xx4 whose one of the principal diagonal elements is 4 is _______ .

The diagonal elements of a skew-symmetric matrix are:

Let psi_(A) be defined as trace of a matrix which is sum of diagonal elements of a square matrix.psi_(lambda A+mu B)=

Assertion (A) [(7,0,0),(0,7,0),(0,0,7)] is a scalar matrix Reason (R) : if all the elements of the principal diagonal are equal, it is called a scalar matrix

Let M be a square matix of order 3 whose elements are real number and adj(adj M) = [(36,0,-4),(0,6,0),(0,3,6)] , then the absolute value of Tr(M) is [Here, adj P denotes adjoint matrix of P and T_(r) (P) denotes trace of matrix P i.e., sum of all principal diagonal elements of matrix P]

Let A=[(1,0,3),(0,b,5),(-(1)/(3),0,c)] , where a, b, c are positive integers. If tr(A)=7 , then the greatest value of |A| is (where tr (A) denotes the trace of matric A i.e. the sum of principal diagonal elements of matrix A)