Let $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If $A^T + A = I$, then

The inverse of the matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ is:

The value of $\Delta = \begin{vmatrix} 2\sin40^\circ & 2\sin50^\circ \\ -3\cos40^\circ & 3\cos50^\circ \end{vmatrix}$ is:

If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & \lambda & -1 \\ 0 & 4 & 2\lambda \end{vmatrix} = 86$, the sum of the values of $\lambda$ is:

If A be a square matrix of order 3 such that $|A| = 2$, then $|adj(2A)|$ is equal to

Match List–I with List–II

Choose the correct answer from the options given below

If the system of linear equations

$x + 2y - 3z = 1$

$(2p+1)y + z = 2$

$3x + 3z = 5$

has a unique solution, then p can not be equal to