Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], ...

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=kI,` where `k in RR, k != 0 and I`is the identity matrix of order 3. If `q_23=-k/8 and det(Q)=k^2/2,` then

`alpha = 0 , k=8`

`4alpha - k+8=0`

`det(P adj(Q))=2^9`

`det(Q adj(P))=2^13`

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