Explanation:

Let’s break it down:

- The matrix A is

```

[  2sin?     cos?    0  ]

[ -2cos?    sin?    0  ]

[  -1             1      1  ]

```

- To find A(adjA), remember: For any square matrix A, A * adj(A) = |A| * I, where |A| is the determinant, and I is the identity.

- So, let’s check det(A):

Calculate using the third row, since there are zeros in the third column, it’s quick:

|A| = (2sin? * sin? - cos? * -2cos?) * 1 = (2sin²? + 2cos²?) = 2 (since sin²? + cos²? = 1).

- Therefore, A(adjA) = 2I.

Now, about your options:

- Null matrix: Only when det(A) = 0, which isn’t the case here.

- -I: Only if det(A) = -1.

- I: Only if det(A) = 1.

- 2I (Correct Answer) ? This matches our calculation.