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What is adjoint of a matrix?

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ADJOINT OF A MATRIX

Let A = [a;j ] be a square matrix of order n and C = [ be its cofactor matrix. Then, matrix CT = [Cji], is called the adjoint of matrix A and is written as

adj (A)=C7 = [C;],153j5n. T .

1 2 3] e.g. If A = -1 0 1 , then C11 = – 3, C12 = 6, C13 = - 3, -

4 4

3 2

C21 =5, C22 = -10, C23 = 5 C31 = 2, C32 = – 4 and C33 = 2 -3 6 -3 -

:: C= 5 -10

5

2

4

2 -3

5

Thus, adj (A)=C7

2

6 -10 -4

---3

5

2

cj]

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