Question:
Four friends Abhay, Bina, Chhaya, and Devesh were asked to simplify \( 4 AB + 3(AB + BA) - 4 BA \), where \( A \) and \( B \) are both matrices of order \( 2 \times 2 \). It is known that \( A \neq B \) and \( A^{-1} \neq B \). Their answers are given as:
Four friends Abhay, Bina, Chhaya, and Devesh were asked to simplify \( 4 AB + 3(AB + BA) - 4 BA \), where \( A \) and \( B \) are both matrices of order \( 2 \times 2 \). It is known that \( A \neq B \) and \( A^{-1} \neq B \). Their answers are given as:
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When simplifying matrix expressions, carefully distribute constants and combine like terms.
Updated On: Mar 8, 2025
- Abhay: \( 6 AB \)
- Bina: \( 7 AB - BA \)
- Chhaya: \( 8 AB \)
- Devesh: \( 7 BA - AB \)
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The Correct Option is B
Solution and Explanation
First, simplify the expression \( 4 AB + 3(AB + BA) - 4 BA \):
\[
4 AB + 3(AB + BA) - 4 BA = 4 AB + 3 AB + 3 BA - 4 BA = 7 AB - BA
\]
Therefore, the correct answer is \( 7 AB - BA \), which is Bina's answer.
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