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Determinants, Adjoint & Inverse · Question 80 of 87

Question 80

EasyOriginal question

AA is invertible and AX=BAX = B. Which of these gives XX?

Options for question 80

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Multiply AX=BAX = B on the left by A−1A^{-1}: A−1AX=A−1BA^{-1}AX = A^{-1}B.

  2. A−1A=IA^{-1}A = I and IX=XIX = X, so X=A−1BX = A^{-1}B.

Worth noting

BA−1BA^{-1} multiplies on the wrong side; for a column BB it is not even defined.

Concept
Why X = A⁻¹B
Typical time
60 s
Your time
—
The rule this testsSolving equations by the matrix method
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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.