Find lambda and that 2 0 1 0 1 2 7 0 1 lambda 0 lambda 14 la

Find lambda and that [2 0 1 0 1 -2 7 0 1] [-lambda 0 lambda 14 lambda 1 -4 lambda 7 lambda 6 -2 lambda] = I_3

Solution

Multiplying the first row of first matrix with the first column of the secon matrix we to get first tem of the identity matrix we get
2*(-x) +0*0 + 7*x = 1
5x=1 meaning x=1/5

but going for the multiplication of second row and third column to get the corresponding element in dientity matrix =0; we get 0*7x +1*6+0*(-2x) = 0 meaning 6=0 which cannot be possible.

Hence there exists no such value of \'x\' for which the product of these 2 matrices is an identity matrix.