Short Quiz

If a matrix B is such that \(\mathrm{B}\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]=\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 1 & 1 \\ 2 & 0 & 1\end{array}\right]\), then the order of matrix B is :

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?

If A and B are skew-symmetric matrices of same order, then \(\mathrm{AB}^{\prime}+\mathrm{BA}^{\prime}\) is a/an :

If A and B are square matrices of order m such that \(\mathrm{A}^2-\mathrm{B}^2=(\mathrm{A}-\mathrm{B})(\mathrm{A}+\mathrm{B})\), then which of the following is always correct?