1. If $x\begin{bmatrix}1\\ 2\end{bmatrix}+y\begin{bmatrix}2\\ 5\end{bmatrix}=\begin{bmatrix}4\\ 9\end{bmatrix}$, then

5. The value $|\begin{matrix}x+y & y+z & z+x\\ z & x & y\\ 1 & 1 & 1\end{matrix}|$ is :

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 \(2\times2\). 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?

Let A be a square matrix of order 3. If \(|A|=5\), then \(|\operatorname{adj} A|\) is:

If A and B are two non-zero square matrices of same order such that \((A+B)^{2}=A^{2}+B^{2}\) then :