AP EAMCET2011MathematicsMatrices
A= [ array lll 1 & 0 & 1 0 & 1 & 1 0 & 1 & 0 array ] A^2-2 A=
Options
- AA⁻¹
- B-A⁻¹
- CI
- D-I
Correct answer
B. -A⁻¹
Step-by-step solution
Given, A= [ array lll 1 & 0 & 1 0 & 1 & 1 0 & 1 & 0 array ] A^2-2 A= [ array lll 1 & 1 & 1 0 & 2 & 1 0 & 1 & 1 array ]- [ array lll 2 & 0 & 2 0 & 2 & 2 0 & 2 & 0 array ] aligned Now, |A| & =1(0-1)-0+1(0)=-1 C₁₁ & =-1, C₁₂=0, C₁₃=0 C₂₁ & =-(-1)=1, C₂₂=0, C₂₃=-1 C₃₁ & =-1, C₃₂=-(1), C₃₃=1 A⁻¹ & =-1 [ array rrr -1 & 1 & -1 0 & 0 & -1 0 & -1 & 1 array ] aligned From Eq. (i) A^2-2 A=-A⁻¹