It is known that \(A\ne B\ne I\) and \(A^{-1}\ne B\).
Their answers are given as:
Abhay: \(6 AB\),
Bina : \(7 AB-BA\),
Chhaya: \(8 AB\),
Devesh: \(7 BA - AB\).
Who answered it correctly?
=\(4~AB+3AB+3BA-4~BA\)
\(=7AB-BA\)
Hence Bina answered it correctly
The given expression is \(4AB + 3(AB + BA) - 4BA\).
Expanding the expression, we get \(4AB + 3AB + 3BA - 4BA\).
Combining like terms, we have \((4AB + 3AB) + (3BA - 4BA)\).
Simplifying further, we get \(7AB - BA\).
Comparing the simplified expression with the answers given by the four friends, we find that Bina's answer, \(7AB - BA\), matches our result.
Correct Answer: Bina
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