The inverse of the matrix [ array ccc 7 & -3 & -3 -1 & 1 & 0 -1 & 0 & 1 array ] is

Step-by-step solution

Let A= [ array ccc 7 & -3 & -3 -1 & 1 & 0 -1 & 0 & 1 array ] Now, aligned |A| & =7(1-0)+3(-1-0)-3(0+1) & =1 aligned Cofactors of matrix A are aligned C₁₁ & =1, C₁₂=1, C₁₃=1 C₂₁ & =3, C₂₂=4, C₂₃=3 C₃₁ & =3, C₃₂=3, C₃₃=4 adj (A) & = [ array lll 1 & 1 & 1 3 & 4 & 3 3 & 3 & 4 array ]^T & = [ array lll 1 & 3 & 3 1 & 4 & 3 1 & 3 & 4 array ] A⁻¹ & = adj (A) |A| = [ array lll 1 & 3 & 3 1 & 4 & 3 1 & 3 & 4 array ] aligned