Q. 395.0( 3 Votes )

If |A| = 2, where

Answer :

We are given that,

Order of matrix A = 2 × 2

|A| = 2

We need to find the |adj A|.

Let us understand what adjoint of a matrix is.

Let A = [aij] be a square matrix of order n × n. Then, the adjoint of the matrix A is transpose of the cofactor of matrix A.

The relationship between adjoint of matrix and determinant of matrix is given as,

|adj A| = |A|n-1

Where, n = order of the matrix

Putting |A| = 2 in the above equation,

|adj A| = (2)n-1 …(i)

Here, order of matrix A = 2

, n = 2

Putting n = 2 in equation (i), we get

|adj A| = (2)2-1

|adj A| = (2)1

|adj A| = 2

Thus, the |adj A| is 2.

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