Finding the adjugate of a 2×2 matrix

[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 )

adjoint .

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 $A = det(A)I/ A^-$

 

[cristo]

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

 

[Charles007]

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

Just remember it? right?

 

[rock.freak667]

Just remember it? right?

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

 

[Charles007]

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

OK. thx.