Let `B` is adjoint of matrix `A` ,having order `3` and `B^(T)B^(-1)=A` (where `B` is non singular),then ,`(tr(A+B))/(4)` is (where `tr(A)` is sum of diagonal elements of matrix `A`)

|A^(-1)|!=|A+^(-1) , where A is a non singular matrix.

Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I, where i is a 2 xx 2 identity matrix, Tr(A) i= sum of diagonal elements of A and |A| = determinant of matrix A. Statement 1:Tr(A)=0 Statement 2: |A| =1

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

Elements of a matrix A of order 10 x 10 are defined as a_(ij)=omega^(i+j) (where omega is cube root unity), then tr(A) of matrix is

For xgt 0. " let A"=[(x+(1)/(x),0,0),(0,1//x,0),(0,0,12)], B=[((x)/(6(x^(2)+1)),0,0),(0,(x)/(4),0),(0,0,(1)/(36))] be two matrices and C=AB+(AB)^(2)+….+(AB)^(n). Then, Tr(lim_(nrarroo)C) is equal to (where Tr(A) is the trace of the matrix A i.e. the sum of the principle diagonal elements of A)

Let A*B=A^(T)B^(-1) where A^(T) represents transpose of matrix A and B^(-1) represents inverse of square matrix B . This operation is defined when the number of rows of A is equal to the number of rows of B . Matrix A is said to be orthogonal if A^(-1)=A^(T) If A*B is defined then which of the following operations are always define?

Let A and B be two matrices such that the order of A is 5xx7 . If A^(T)B and BA^(T) are both defined, then (where A^(T) is the transpose of matrix A)

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

If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is an identity matrix of same order as of A )

Let A be a non - singular symmetric matrix of order 3. If A^(T)=A^(2)-I , then (A-I)^(-1) is equal to