Adjoint And Inverse Of A Matrix

Given the matrix , we need to find the value of .

The adjugate of a matrix, , is equal to the cofactor matrix of transposed. For a matrix, if is a diagonal matrix like the one given, every diagonal element contributes to the determinant and adjugate in a specific pattern.

The determinant of a diagonal matrix is the product of its diagonal elements, so:

For a matrix, the property holds. Since is a diagonal matrix, its inverse can be easily defined as:

Hence, the adjugate is:

The determinant of is the product of its diagonal elements:

Thus, .

• , the determinant of .
• .