# Write the adjoint of the following matrix $\begin{bmatrix} 2 & -1 \\ 4 & 3 \end{bmatrix}$

## 1 Answer

Toolbox:
• The determinant value of a $2\times 2$ square matrix is $|A|=a_{12} \times a_{22} - a_{21} \times a_{12}$
• The inverse of a $2 \times 2$ square matrix is $\frac{1}{|A|} \begin{bmatrix} a_{22} & -a_{12} \\ a_{21} & a_{11} \end{bmatrix}$
Adjoint of a $2 \times 2$ matrix can be found by interchanging the elements of $a_{11}\; and \;a_{22}$ and changing the symbols of elements of $a_{21}\; and\; a_{12}$
Given $A= \begin{bmatrix} 2 & -1 \\ 4 & 3 \end{bmatrix}$
By using the above hint we get
$adj(A)= \begin{bmatrix} 3 & 1 \\ -4 & 2 \end{bmatrix}$

answered Apr 8, 2013 by

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