If $A = \begin{bmatrix} 6 & 4 \\ 5 & 3 \end{bmatrix}$ and $B = adj(A)$, then $|B|$ is equal to:

If $A=\begin{bmatrix}1 & 2 & 2\\2 & 1 & -2\\\alpha & 2 & \beta\end{bmatrix}$ and $AA^T=9I$, where I is the identity matrix of order 3, then $(\beta-\alpha)$ equals:

If $P=\left[\begin{array}{r}-1 \\ 2 \\ 1\end{array}\right]$ and $Q=\left[\begin{array}{lll}2 & -4 & 1\end{array}\right]$ are two matrices, then $(P Q)^{\prime}$ will be :

The linear equation involving $x$ and $y$ are written in matrix form as:

If $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 0 & 2 \\ x & 1 & 1 \end{bmatrix}$ and $A^{-1} = \frac{1}{4}\begin{bmatrix} -2 & 0 & y \\ 5 & -2 & -1 \\ 1 & 2 & -1 \end{bmatrix}$, then values of x and y, are:

If $A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to

If $\begin{vmatrix} -1 & a & a^2 \\ -1 & b & b^2 \\ -1 & c & c^2 \end{vmatrix}^2 = \lambda$ and $a - b = 1$, $b - c = 2$ and $c - a = 3$, then the value of $\lambda$ is