# Any one help. Adjugate of 2X2 matrix

1. Sep 2, 2009

### Charles007

I know how to find the adjugate of 3x3 matrix. from the defination.

How to find adjugate of 2x2 matrix.

e.g A= ( 1 3 )
______( 2 4 )

I know how to find adjugate and inverse. of 3 * 3 matrix

First . I find matrix of cofactor. from the defination. (n-1)(n-1) matrix * (sign associated with the element's position).

Second, we taking the transpose we get the adj(A)

Then we find the det(A).

Finally, A^-1 = 1/det(A) * adj(A)

The inverse of A.

$AA^- = A^-A=I$ and A adj(A) = det(A)I

The inverse of $A = det(A)I/ A^-$

2. Sep 2, 2009

### cristo

Staff Emeritus
Isn't $$\text{adj}\left(\begin{array}{cc}a&b\\c&d\end{array}\right)=\left(\begin{array}{cc}d&-b\\-c&a\end{array}\right)$$?

3. Sep 2, 2009

### Charles007

Just remember it? right?

4. Sep 2, 2009

### rock.freak667

yes, that is it for a 2x2 matrix, switch elements 1 and 4; change the sign of elements 2 and 3

5. Sep 3, 2009

### Charles007

OK. thx. :rofl: