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Determinants, Adjoint & Inverse · Question 51 of 87

Question 51

MediumOriginal question

AA is a square matrix of order 3 with ∣A∣=6|A| = 6. Which matrix is A(adj⁡A)A(\operatorname{adj} A)?

Options for question 51

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. For every square matrix, A(adj⁡A)=(adj⁡A)A=∣A∣IA(\operatorname{adj} A) = (\operatorname{adj} A)A = |A|I.

  2. Here that is 6I6I.

Worth noting

36I36I mixes in ∣adj⁡A∣=∣A∣2=36|\operatorname{adj} A| = |A|^2 = 36, which is a number about the adjoint, not this product.

Concept
The product of a matrix and its adjoint
Typical time
90 s
Your time
—
The rule this testsThe adjoint and the inverse
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Ten questions from Determinants, Adjoint & Inverse, at your own pace.

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Ten questions from Determinants, Adjoint & Inverse, at your own pace.