Let `p=[(3,-1,-2),(2,0,alpha),(3,-5,0)],` where `alpha in RR.` Suppose `Q=[q_(ij)]` is a matrix such that `PQ=kl,` where `k in RR, k != 0 and l` is the identity matrix of order 3. If `q_23=-k/8 and det(Q)=k^2/2,` then

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 k is a scalar and l is a unit matrix of order 3 then adj(kl) is equal to

If A=[(1,0),(-1,7)] and l is an identity matrix of order 2, then the value of k, if A^(2)=8A+kI , is :

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

If A is 3x3 matrix and det adj(A)=k then det(adj2A)=

Let P=[(2alpha),(5),(-3alpha^(2))] and Q=[(2l,-m,5n)] are two matrices, where l, m, n, alpha in R , then the value of determinant PQ is equal to

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

[[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=