If \( A = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \), then what is the value of \( \det(I + AA') \), where \( I \) is the \( 3 \times 3 \) identity matrix?
Let A be a skew-symmetric matrix of order 3. What is the value of \( \det(4A^{4}) - \det(3A^{3}) + \det(2A^{2}) - \det(A) + \det(-I) \), where I is the identity matrix of order 3?
A. \( A^{2} \) is symmetric matrix with \( \det(A^{2}) = 0 \).
9.
If
\( A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix} \)
then which of the following statements are correct?
1. \( A^{n} \) will always be singular for any positive integer \( n \).
2. \( A^{n} \) will always be a diagonal matrix for any positive integer \( n \).
3. \( A^{n} \) will always be a symmetric matrix for any positive integer \( n \).
Select the correct answer using the code given below:
