`A=[[0 ,1],[ 3 ,0]]a n d(A^8+A^6+A^4+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 _____.

Let A=[(0,1),(2,0)] and (A^(8)+A^(6)+A^(2)+I)V=[(32),(62)] where I is the (2xx2 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

If A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)] , then verify that A^2+A=A(A+I) , where I is the identity matrix.

Let A=[[0, 1],[ 0, 0]] show that (a I+b A)^n=a^n I+n a^(n-1)b A , where I is the identity matrix of order 2 and n in N .

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 ________.

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

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

If [[2,-1],[1,0],[-3,4]]A=[[-1,-8,-10],[1,-2,-5],[9,22,15]] , then sum of all the elements of matrix A is

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 )