If $A=\left[\begin{array}{ccc}\sin 2 \theta & 2 \sin ^2 \theta-1 & 0 \\ \cos 2 \theta & 2 \sin \theta \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$, then which of the following statements is/are correct?

1. $A^{-1}=\operatorname{adj} A$

2. A is skew-symmetric matrix

3. $A^{-1}=A^T$

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If $A=\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{array}\right]$, then which of the following statements are correct?

1. An will always be singular for any positive integer n.

2. An will always be a diagonal matrix for any positive integer n.

3. An will always be a symmetric matrix for any positive integer n.

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If $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$, then what is 23A3 - 19A2 - 4A equal to ?

Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (AB - BA) ?

1. Its diagonal entries are equal but nonzero

2. The sum of its non-diagonal entries is zero

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