To find adjoint of a 2x2 matrix, we have to be aware of primary and secondary diagonals of a 2x2 matrix.
For instance,
To find adjoint of a 2x2 matrix, we have to switch the elements of the primary diagonal and change the signs of the elements of the secondary diagonal.
Therefore,
Example 1 :
Find the adjoint of the following matrix.
Solution :
Consider the following 3x3 matrix.
Let A_{ij} be the cofactor matrix of A.
Where
and so on.
Therefore,
adj A = (A_{ij})^{T}
Example 2 :
Find the adjoint of the following matrix.
Solution :
Find the cofactor of each element.
Cofactor of 1 :
Cofactor of 1 :
Cofactor of 1 :
Cofactor of 1 :
Cofactor of 2 :
Cofactor of -3 :
Cofactor of 2 :
Cofactor of -1 :
Cofactor of 3 :
The cofactor matrix of A is
Therefore,
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