If $A+B = \begin{bmatrix}7 & 0\\2 & 5\end{bmatrix}$ and $A-B = \begin{bmatrix}3 & 0\\0 & 3\end{bmatrix}$, then

If A is a square matrix of order 3 with $|A| = 4$, then the value of $|2\,adj\,A|$ is:

If the matrix $\begin{bmatrix}2 & -1 & 3\\ \lambda & 0 & 7\\-1 & 1 & 4\end{bmatrix}$ is not invertible, then value of $\lambda$ is

If $[1 \quad 2 \quad 1] \begin{bmatrix} -1 & 0 & 1 \\ 1 & 2 & -1 \\ 0 & 1 & 3 \end{bmatrix} \begin{bmatrix} 2x \\ x \\ -7 \end{bmatrix} = [0]$, then the value of $x$ is

If the points (a, b), (c, d) and (a + c, b + d) are collinear, then

Let $A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ and $I$ be an identity matrix of order 3. If $A^TA=I$, then $x^2+y^2+z^2$ is equal to:

Let A be the square matrix of order 3, then |kA|, where k is a scalar, is equal to: