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Determinants, Adjoint & Inverse · Question 20 of 87

Question 20

MediumOriginal question

If A=[2134]A = \begin{bmatrix}2 & 1 \\ 3 & 4\end{bmatrix} and B=[1−223]B = \begin{bmatrix}1 & -2 \\ 2 & 3\end{bmatrix}, what is ∣AB∣|AB|?

Options for question 20

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. ∣AB∣=∣A∣∣B∣|AB| = |A||B|.

  2. ∣A∣=8−3=5|A| = 8 - 3 = 5 and ∣B∣=3+4=7|B| = 3 + 4 = 7, so ∣AB∣=35|AB| = 35.

Worth noting

12 adds the determinants; the determinant of a product multiplies them.

Concept
Determinant of a product
Typical time
90 s
Your time
—
The rule this testsThe determinant of a matrix
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