Find the inverse of the matrix $A$ using minors, cofactors and adjugate.
$A = [\begin{array}{ccc} 0 & 2 & 2 \\ 6 & 4 & - 1 \\ 1 & - 1 & - 1 \end{array}]$

Answer

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Answer

$A^{- 1} = (\begin{array}{lll} 0.5 & 0.25 & - 0.67 \\ 0.25 & 0.17 & - 0.33 \\ - 1.17 & - 0.58 & 1.17 \end{array})$

Steps

Step 1 ：Find the determinant of the matrix $A$ : $det (A) = - 12$

Step 2 ：Since the determinant is non-zero, the inverse of $A$ exists.

Step 3 ：Find the adjugate of the matrix $A$ : $adj (A) = (\begin{array}{lll} - 6 & - 3 & 8 \\ - 3 & - 2 & 4 \\ 14 & 7 & - 14 \end{array})$

Step 4 ：Calculate the inverse of $A$ using the formula: $A^{- 1} = \frac{1}{det (A)} adj (A)$

Step 5 ： $A^{- 1} = (\begin{array}{lll} 0.5 & 0.25 & - 0.67 \\ 0.25 & 0.17 & - 0.33 \\ - 1.17 & - 0.58 & 1.17 \end{array})$