Let's consider a 2x2 matrix as an example and find its adjoint.
Consider the matrix A:
A = [
a b
c d
]
The adjoint of a 2x2 matrix is found by swapping the positions of the elements in the main diagonal (a and d) and changing the signs of the other two elements (b and c).
The adjoint matrix, denoted as adj(A), is given by:
adj(A) = [
d -b
-c a
]
Here's an example:
Let A = [
2 3
1 4
]
Swap the positions of elements a and d:
adj(A) = [
4 3
1 2
]
Change the signs of elements b and c:
adj(A) = [
4 -3
-1 2
]
So, the adjoint matrix of A = [ 2 3 1 4 ] is [ 4 -3 -1 2 ].