The element in the third row and first column of the inverse of the matrix [ array ccc 1 & -3 & 2 -3 & 3 & -1 2 & -1 & 0 array ] is

Step-by-step solution

We have A= [ array ccc -1 & -3 & 2 -3 & 3 & -1 2 & -1 & 0 array ] aligned |A| &= | array ccc -1 & -3 & 2 -3 & 3 & -1 2 & -1 & 0 array | &=-(-1)+3(2)+2(3-6)=1+6-6=1 aligned We have to find a₃₁ in A⁻¹ . So we will find A₁₃ in A . Cofactor of 2=(-1)¹⁺³ | array cc -3 & 3 2 & -1 array |=3-6=-3 Hence a₃₁ in A⁻¹= -3 |A| = -3 1 =-3