For the matrix A= [ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] A⁻¹=

Step-by-step solution

Given, aligned & Given, A= [ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] & Now, |A|= [ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array . & =3(-3+4)+3(2-0)+4(-2-0)=3+6-8=1 0 aligned Here, aligned & A₁₁=1, A₁₂=-2, A₁₃=-2 & A₂₁=-1, A₂₂=3, A₂₃=3 & A₃₁=0, A₃₂=-4, A₃₃=-3 aligned adj (A)= [ array ccc 1 & -2 & -2 -1 & 3 & 3 0 & -4 & -3 array ]^1= [ array ccc 1 & -1 & 0 -2 & 3 & -4 -2 & 3 & -3 array ] Now, aligned A⁻¹ & = adj (A) |A| = [ array ccc 1 & -1 & 0 -2 & 3 & -4 -2 & 3 & -3 array ] A^2 & =A A= [ array lll 3