Question

For an invertible matrix A, if A (adj A) = `|(20, 0),(0, 20)|`, then | A | = ______.

विकल्प

• 20

• – 200

• 200

• – 20

Answer 1

For an invertible matrix A, if A (adj A) = `|(20, 0),(0, 20)|`, then | A | = 20.

Explanation:

Given, A (adj A) = `|(20, 0),(0, 20)|`

`20|(1, 0),(0, 1)|` = 20 I

We know that

A^–1 = `1/|A| adj A`

`\implies` A (adj A) = | A | I

`\implies` 20I =  | A | I

`\implies` | A | = 20