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 of matrices of order 3xx3 such that all elemtns of the matrix belong to {0,1} let E_(1)={A in S:|A|=0} where |A| denotes determinant of matrix A E_(2)={A in S: sum of elements of A=7 } find P(E_(1)//E_(2))

Let p be a non singular matrix,and I+P+p^(2)+...+p^(n)=0, then find p^(-1)

Let P be the set of all non-singular matrices of order 3 over and Q be the set of all orthogonal matrices of order 3 over.Then,

Let P be a non - singular matrix such that I+P+P^(2)+…….P^(n)=O (where O denotes the null matrix), then P^(-1) is

Consider the system of linear equations - x + y + 2z = 0 3x - ay + 5z = 1 2x - 2y - az = 7 Let S_1 be the set of all a in R for which the system is inconsistent and S_2 be the set of all a in R for which the system has infinitely many solutions. If n(S_1) and n(S_2) denote the number of elements in S_1 and S_2 respectively, then

Consider the system of linear equations - x + y + 2z = 0 3x - ay + 5z = 1 2x - 2y - az = 7 Let S_1 be the set of all a in R for which the system is inconsistent and S_2 be the set of all a in R for which the system has infinitely many solutions. If n(S_1) and n(S_2) denote the number of elements in S_1 and S_2 respectively, then

Let P be the set of all non - singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 over R. Then