which of the following represents the inverse of the matrix below?\n$a = \\begin{bmatrix}a&b\\c&d\\end{bmatri…

which of the following represents the inverse of the matrix below?\n$a = \\begin{bmatrix}a&b\\c&d\\end{bmatrix}$\n$\\frac{1}{|a|}\\begin{bmatrix}-d&b\\c&-a\\end{bmatrix}$\n$\\frac{1}{|a|}\\begin{bmatrix}d&-b\\-c&a\\end{bmatrix}$\n$\\frac{1}{|a|}\\begin{bmatrix}d&-c\\-b&a\\end{bmatrix}$\n$\\frac{1}{|a|}\\begin{bmatrix}a&-b\\-c&d\\end{bmatrix}$

which of the following represents the inverse of the matrix below?\n$a = \\begin{bmatrix}a&b\\c&d\\end{bmatrix}$\n$\\frac{1}{|a|}\\begin{bmatrix}-d&b\\c&-a\\end{bmatrix}$\n$\\frac{1}{|a|}\\begin{bmatrix}d&-b\\-c&a\\end{bmatrix}$\n$\\frac{1}{|a|}\\begin{bmatrix}d&-c\\-b&a\\end{bmatrix}$\n$\\frac{1}{|a|}\\begin{bmatrix}a&-b\\-c&d\\end{bmatrix}$

Answer

Explanation:

Step1: Recall inverse - matrix formula

For a (2\times2) matrix (A=\begin{bmatrix}a&b\c&d\end{bmatrix}), the inverse (A^{-1}=\frac{1}{\text{det}(A)}\text{adj}(A)), where (\text{det}(A)=ad - bc) and the adjugate of (A), (\text{adj}(A)=\begin{bmatrix}d&-b\-c&a\end{bmatrix}).

Answer:

B. (\frac{1}{|A|}\begin{bmatrix}d&-b\-c&a\end{bmatrix})