Short Quiz

Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify \(4 \mathrm{AB}+3(\mathrm{AB}+\mathrm{BA})-4 \mathrm{BA}\), where A and B are both matrices of order \(2 \times 2\). It is known that \(A \neq B \neq I\) and \(A^{-1} \neq B\).
Their answers are given as :
Abhay : 6 AB
Bina : \(7 \mathrm{AB}-\mathrm{BA}\)
Chhaya: 8 AB
Devesh : 7 BA - AB
Who answered it correctly?

Assertion (A) : Every scalar matrix is a diagonal matrix.
Reason (R) : In a diagonal matrix, all the diagonal elements are 0 .

For any square matrix A , (A \(-\mathrm{A}^{\prime}\) ) is always

If \(A=\left[a_{i j}\right]\) is an identity matrix, then which of the following is true ?