Adjoint Of A Matrix

Step 1: Recall the 2 2 formula. For , This comes from taking cofactors and then transposing the cofactor matrix (for a , that reduces to swapping and negating the off–diagonals). \\ [4pt]

Step 2: Apply it to . Here . Therefore This matches option (A).

To find the adjoint of a matrix, we first calculate the cofactor matrix and then transpose it. Given matrix , we will find the cofactor matrix by finding the minors and then the cofactors: - For the (1,1) element: The minor is the determinant of , which is 4. The cofactor is . - For the (1,2) element: The minor is the determinant of , which is 5. The cofactor is . - For the (2,1) element: The minor is the determinant of , which is 3. The cofactor is . - For the (2,2) element: The minor is the determinant of , which is 2. The cofactor is . Thus, the cofactor matrix is: Now, we take the transpose of the cofactor matrix to get the adjoint matrix, which remains the same in this case. Therefore, the adjoint is: