Matrices And Determinants

For a 2×2 matrix the inverse is given by:

Here, , , , .

Determinant:

Now substitute into the formula:

Simplify each element:

Hence, the inverse of the given matrix is:

First, calculate :

Next, calculate :

Now subtract from :

Simplify by subtracting corresponding elements:

Therefore, the result is:

Correct Answer:

(C)

To find the transpose of a matrix , we interchange its rows and columns. The transpose is denoted by .

The given matrix is:

The first row of , , becomes the first column of . The second row, , becomes the second column of .

Therefore, the transpose of is:

Hence, the correct answer is:

Correct Answer:

(C)

From the given equation: Rearranging for :

Step 1: Calculate

Step 2: Calculate

Step 3: Substitute into

Therefore, the required matrix is:

Correct Answer:

(C)