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Determinants, Adjoint & Inverse · Question 7 of 87

Question 7

EasyOriginal question

AA is a square matrix of order 3 with ∣A∣=5|A| = 5. What is ∣2A∣|2A|?

Options for question 7

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. 2A2A multiplies each of the 3 rows of AA by 22, and each row brings out one factor 22.

  2. ∣2A∣=23∣A∣=8×5=40|2A| = 2^{3}|A| = 8 \times 5 = 40.

Worth noting

1010 takes the factor out once; it comes out once for each row.

Concept
Determinant of a scalar multiple
Typical time
60 s
Your time
—
The rule this testsThe determinant of a matrix
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Ten questions from Determinants, Adjoint & Inverse, at your own pace.

Practise this chapter →

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