# Cofactor of matrix calculator

To find the cofactor matrix of a given matrix, follow these steps:

1. For each element in the original matrix, determine the submatrix formed by removing the row and column containing that element.
2. Calculate the determinant of each submatrix.
3. Multiply each determinant by (-1)^(i+j), where i and j are the row and column numbers of the element being removed.
4. Place the resulting values in a new matrix to form the cofactor matrix.

Here’s an example of how to find the cofactor matrix of a 3×3 matrix:

Let’s say we have the matrix:

[1 2 3]

[4 5 6]

[7 8 9]

1. For the element in the first row and first column (1), the submatrix formed by removing that row and column is:

[5 6]

[8 9]

1. The determinant of this submatrix is (59 – 68) = -3.
2. Multiply this determinant by (-1)^(1+1) = 1 to get -3.
3. Place this value in the first row and first column of the cofactor matrix.

Repeat these steps for each element in the matrix to obtain the full cofactor matrix. The resulting cofactor matrix will have the same dimensions as the original matrix.

If you would like to use a calculator to find the cofactor matrix, you can use any online matrix calculator that supports this operation. Simply input the matrix, select the option to find the cofactor matrix, and the calculator will do the work for you.