Let `P=[[1,0,0],[4,1,0],[16,4,1]]`and `I` be the identity matrix of order `3`. If `Q = [q_()ij ]` is a matrix, such that `P^(50)-Q=I`, then `(q_(31)+q_(32))/q_(21)` equals

Let P=[[1,0,04,1,016,4,1]] and I be the identity matrix of order 3. If Q=[qij] is a matrix, such that P^(50)-Q=I, then (q_(31)+q_(32))/(q_(21)) equals

[[2,3,5],[4,1,2],[1,2,1]]=P+Q , where P is a symmetric matrix and Q is a skew symmetric matrix then Q=

If P=[(lambda,0),(7,1)] and Q=[(4,0),(-7,1)] such that P^(2)=Q , then P^(3) is equal to

Let A=[[0,2q,r] , [p,q,-r] , [p,-q,r]] If A A^T=I_3 then |p|=

Let P=[(3,-1,-2),(2,0,alpha),(3,-5,0)] , where alpha in R . Suppose Q =[q_(ij)] is a matrix satisfying PQ = KI_3 for some non - zero K in R . If q_(23) =- (K)/(8) and |Q| = (1)/(2), then alpha^2 + k^2 is equal to ________.

If A=[{:(6,0),(p,q):}] is a scalar matrix then the value of p and q are

Let A = [[2,3],[a,0]], a in R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to :

If the points (0,0),(3,3),(p,q) form an equilateral triangle and q_(1),q_(2) are the two values of q then q_(1)+q_(2)=