ADJOINT OF A MATRIX

Adjoint of a 2x2 Matrix

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 :

Adjoint of a 3x3 Matrix

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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