`A=[[0 ,1],[ 3 ,0]]a n dA^8+A^6+A^2+I V=[[0] ,[11]](w h e r eIi s` the `2xx2` identity matrix`),` then the product of all elements of matrix `V` is _____.

A=[[0,1],[3,0]]" and let "BV=[[0],[11]]" Where "B=A^(8)+A^6+A^(4)+A^(2)+I," (Where "I" is the "2times2" identity matrix) then the product of all elements of matrix "V" is "

If A = [[0, 1],[3,0]]and (A^(8) + A^(6) + A^(4) + A^(2) + I) V= [[0],[11]], where V is a vertical vector and I is the 2xx2 identity matrix and if lambda is sum of all elements of vertical vector V , the value of 11 lambda is

Let A=[(2,0,7),(0,1,0),(1,-2,1)] and B=[(-k,14k,7k),(0,1,0),(k,-4k,-2k)] . If AB=I , where I is an identity matrix of order 3, then the sum of all elements of matrix B is equal to

A is a 2 x 2 matrix, I is 2 x 2 identity matrix. IA - xIl=0 has the roots -1, 3. Then the sum of diagonal elements of A^2

Let S be the set which contains all possible vaues fo I ,m ,n ,p ,q ,r for which A=[I^2-3p0 0m^2-8q r0n^2-15] be non-singular idempotent matrix. Then the sum of all the elements of the set S is ________.

If A = [(1,1,1),(0,1,1),(0,0,1)] and M = A + A^(2) + A^(3) + . . . . + A^(20) then the sum of all the elements of the matrix M is equal to _____

Let A be a 2xx2 matrix with non zero entries and let A^(2)=I , where I is 2xx2 identity matrix. Define Tr(A)= sum of diagonal elemets of A and |A|= determinant of matrix A. Statement 1: Tr(A)=0 Statement 2: |A|=1 .

If is a 2 xx 2 identity matrix, then | (3I)^(30)|^(-1) =_____.

If A is a square matrix and |A|!=0 and A^(2)-7A+I=0 ,then A^(-1) is equal to (I is identity matrix)