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Question
Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4AB + 3(AB + BA) − 4BA, where A and B are both matrices of order 2 × 2. It is known that A ≠ B ≠ I and A−1 ≠ B.
Their answers are given as:
Abhay: 6AB
Bina: 7AB − BA
Chhaya: 8 AB
Devesh: 7BA − AB
Who answered it correctly?
Options
Abhay
Bina
Chhaya
Devesh
MCQ
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Solution
Bina
Explanation:
4AB + 3(AB + BA) – 4ВА
= 4AB + ЗАВ + ЗВА – 4ВА
= 7AB – ВА (∵ АB ≠ BА multiplication is not commutative)
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