Each element which is associated with a 2*2 determinant then the values of that determinant are called cofactors. The cofactor is defined the signed minor. An (i,j) cofactor is computed by multiplying (i,j) minor by and is denoted by . The formula to find cofactor = where denotes the minor of row and column of a matrix.

## Co-factor of 2×2 order matrix

Let A be a square matrix. By cofactor of an element of A, we mean minor of with a positive or negative sign depending on i and j. For a 2*2 matrix, negative sign is to be given the minor element and =

**Example 1: **Consider the matrix

**Solution: **The minor of 5 is 2 and Cofactor 5 is 2 (sign unchanged)

The minor of -1 is 2 and Cofactor -1 is -2 (sign changed)

The minor of 2 is -1 and Cofactor -1 is +1 (sign changed)

The minor of 2 is 5 and Cofactor 2 is 5 (sign unchanged)

Co- factor of

**Example 2:** Consider the matrix

**Solution:** The minor of 5 is 0 and Cofactor 5 is 0 (sign unchanged)

The minor of -3 is -2 and Cofactor -3 is +2 (sign changed)

The minor of -2 is -3 and Cofactor -2 is +3 (sign changed)

The minor of 0 is 5 and Cofactor 0 is 5 (sign unchanged)

Co- factor of

## Co-factor of 3×3 order matrix

For a 3*3 matrix, negative sign is to given to minor of element :

**Example 3:** Consider the matrix

**Solution:** Minor of 2 is 7 and Cofactor is 7.

Minor of -3 is 18 and Cofactor is -18 (sign changed)

Minor of -1 is 30 and Cofactor are 30.

Minor of 6 is 1 and Cofactor is -1 (sign changed)

Minor of 4 is 6 and Cofactor are 6.

Minor of 1 is 10 and Cofactor is -10 (sign changed)

Minor of 0 is 1 and Cofactor are 1.

Minor of 6 is 8 and Cofactor is -8 (sign changed)

Minor of 3 is 26 and Cofactor is 26

**Example 4: **Consider the matrix

**Solution: **Minor of 3 is -26 and Cofactor is -26.

Minor of -2 is 18 and Cofactor is -8 (sign changed)

Minor of -1 is 12 and Cofactor is 12.

Minor of 2 is -2 and Cofactor is -2 (sign changed)

Minor of 1 is 12 and Cofactor are 12.

Minor of 5 is 18 and Cofactor is -18 (sign changed)

Minor of 0 is -9 and Cofactor are -9.

Minor of 6 is 17 and Cofactor is -17 (sign changed)

Minor of 4 is 7 and Cofactor are 7.

## Exercise

- Find the co-factors of the matrix .
- Find the co-factors of matrix .
- Find the co-factors of matrix.
- Find the co-factors of matrix .
- Find the co-factors of the matrix .

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