If A = ((3,4,1),(1,0,-2),(-2,-1,2))then A^{-1} = ? ​

Question

If A = \( \begin{pmatrix} 3&4&1 \\ 1 &0&-2\\-2&-1&2 \end{pmatrix}\)then A^-1 = ?

A. \( \begin{pmatrix} 2&9&-8 \\ -2&8&7\\-1&5&-4 \end{pmatrix}\)

B.\( \begin{pmatrix} -2&9&-8 \\ -2&8&7\\-1&-5&4 \end{pmatrix}\)

C.\( \begin{pmatrix} -2&-9&-8 \\ 2&8&7\\-1&-5&-4 \end{pmatrix}\)

D. None of these

Answer 1

|A| = 3 x (0 - 2) – 4 x (2-4)+1 x (-1) 

= -6+8-1 

= 1 

C₁₁ = -2 C₁₂ = 2 C₁₃ = -1 

C₂₁ = -9 C₂₂ = 8 C₂₃ = -5 

C₃₁ = -8 C₃₂ = 7 C₃₃ = -4

\( \begin{pmatrix} -2&-9&-8 \\ 2&8&7\\-1&-5&-4 \end{pmatrix}\)