If $A = \begin{bmatrix} 2 \sin \theta & \cos \theta & 0 \\ -2\cos \theta & \sin \theta & 0 \\ -1 & 1 & 1 \end{bmatrix},$ then what is A(adj A) equal to?

(where) I is the identity matrix.

For what value of k is the matrix $\begin{bmatrix} 2\cos 2\theta & 2\cos 2\theta & 6 \\ 1 -2 \sin^2\theta & 2 \cos^2\theta -1 & 3 \\ k & 2k & 1 \end{bmatrix}$ singular?

Let A be a non-singular matrix and B = adj A. Which of the following statements is/are correct?

1. AB = BA

2. AB is a scalar matrix

3. AB can be a null matrix

Select the correct answer using the code given below:

Consider the following statements in respect of square matrices A and B of same order :

1. If AB is a null matrix, then at least one of A and B is a null matrix.

2. If AB is an identity matrix, then BA = AB.

Which of the above statements is/are correct?