Find the inverse of the 2x2 matrix \(A = \begin{bmatrix} 3 & 4 \\ 2 & 1 \end{bmatrix}\).

Step 1 ：The formula to find the inverse of a 2x2 matrix \(A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}\) is given by \(A^{-1} = \frac{1}{{ad - bc}} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\)

Step 2 ：Here, \(a = 3\), \(b = 4\), \(c = 2\), and \(d = 1\). So, \(ad - bc = 3*1 - 4*2 = -5\)

Step 3 ：Substitute these values into the formula to get \(A^{-1} = \frac{1}{{-5}} \begin{bmatrix} 1 & -4 \\ -2 & 3 \end{bmatrix} = \begin{bmatrix} -0.2 & 0.8 \\ 0.4 & -0.6 \end{bmatrix}\)