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Question
For an invertible matrix A, if A (adj A) = `|(20, 0),(0, 20)|`, then | A | = ______.
Options
20
– 200
200
– 20
MCQ
Fill in the Blanks
Solution
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
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