Consider the following statements in respect of a non-singular matrix $A$ of order $n$:
1. $A(\text{adj}A^T) = A(\text{adj}A)^T$
2. If $A^2 = A$, then $A$ is identity matrix of order $n$
3. If $A^3 = A$, then $A$ is identity matrix of order $n$
Which of the statements given above are correct?
Consider the following statements in respect of a skew-symmetric matrix $A$ of order $3$:
1. All diagonal elements are zero.
2. The sum of all the diagonal elements of the matrix is zero.
3. $A$ is orthogonal matrix.
Which of the statements given above are correct?
1. $A^{-1}=\operatorname{adj} A$
2. A is skew-symmetric matrix
3. $A^{-1}=A^T$
Select the correct answer using the code given below :
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.
Select the correct answer using the code given below: