Given the matrix (A = begin{vmatrix} 3 & -2 \ 1 & 6 end{vmatrix}). Find the inverse of matrix A.
- A.
(begin{vmatrix} 6 & 2 \ 1 & 6 end{vmatrix}) - B.
(begin{vmatrix} frac{2}{11} & frac{1}{12}\ frac{3}{20} & frac{1}{10} end{vmatrix}) - C.
(begin{vmatrix} -3 & 2 \ -1 & -6 end{vmatrix}) - D.
(begin{vmatrix} frac{3}{10} & frac{1}{10} \ frac{-1}{20} & frac{3}{20}end{vmatrix})
Correct Answer: Option D
Explanation
(A = begin{vmatrix} 3 & -2 \ 1 & 6 end{vmatrix})
|A| = (3 x 6) – (-2 x 1)
= 18 + 2
= 20.
A(^{-1}) = (frac{1}{20} begin{vmatrix} 6 & 2 \ -1 & 3 end{vmatrix})
= (begin{vmatrix} frac{6}{20} & frac{2}{20} \ frac{-1}{20} & frac{3}{20} end{vmatrix})
= (begin{vmatrix} frac{3}{10} & frac{1}{10} \ frac{-1}{20} & frac{3}{20} end{vmatrix})
There is an explanation video available below.