Given the matrix A = \(\begin{bmatrix} 3 & 4 \\ 2 & 5 \end{bmatrix}\), find the inverse of A.
Answer
Step 4: Then, multiply each element in the matrix by 1/det(A), or 1/7. So, the matrix becomes \(\begin{bmatrix} 5/7 & -4/7 \\ -2/7 & 3/7 \end{bmatrix}\).
Step 1 ：Step 1: Find the determinant of the matrix A, denoted as det(A). It is calculated as (3*5) - (4*2) = 7.
Step 2 ：Step 2: Swap the positions of the elements a11 and a22. So, the matrix becomes \(\begin{bmatrix} 5 & 4 \\ 2 & 3 \end{bmatrix}\).
Step 3 ：Step 3: Change the signs of the elements a12 and a21. So, the matrix becomes \(\begin{bmatrix} 5 & -4 \\ -2 & 3 \end{bmatrix}\).
Step 4 ：Step 4: Then, multiply each element in the matrix by 1/det(A), or 1/7. So, the matrix becomes \(\begin{bmatrix} 5/7 & -4/7 \\ -2/7 & 3/7 \end{bmatrix}\).
