Let P=3-1-220α3-50, where α∈ℝ. Suppose Q=qij is a matrix such that PQ=kI, where k∈ℝ,k≠0 and I is the identity matrix of order 3. If q23=-k8 and det(Q)=k22, then

PQ=KI⇒PQ≠0⇒Q=KP−1P=12α+20∴K22=K3112α+20Q=KP−1=K12α+205α10-α3α6-3α-4-10122Q23=−k8=−k(3α+4)12α+20⇒α=-1,k=4|P(AdjQ)|=|P‖Q|2     since Q=kP-1=k3P-1=k3P=K6P=29Q(AdjP)=QP2=K3P=29