If |A| = 2, where A is 2 × 2 matrix, find |adj A|.

1.	If \|A\| = 2, where A is 2 × 2 matrix, find \|adj A\|.
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 = [a_ij] 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.

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 = [a_ij] 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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