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

Step 1 ：Step 1: Calculate the determinant of A, denoted as det(A). Using the formula, det(A) = ad-bc = \( (1*4) - (2*3) = -2 \)

Step 2 ：Step 2: Swap the positions of a and d. So the matrix becomes \( \begin{bmatrix} 4 & 2 \ 3 & 1 \end{bmatrix} \)

Step 3 ：Step 3: Change the signs of b and c. So the matrix becomes \( \begin{bmatrix} 4 & -2 \ -3 & 1 \end{bmatrix} \)

Step 4 ：Step 4: Multiply each term in the matrix by \(\frac{1}{det(A)}\). So the inverse of A, denoted as A^-1, is \( \frac{1}{-2} \) times \( \begin{bmatrix} 4 & -2 \ -3 & 1 \end{bmatrix} \) which gives \( \begin{bmatrix} -2 & 1 \ 1.5 & -0.5 \end{bmatrix} \)