If $A = \begin{bmatrix}1 & 2\\ 0 & 3\end{bmatrix}$ then $|A. adj A|$ is

Let $A = [a_{ij}]$ be a square matrix, where $a_{ij} = \begin{cases} 0, & \text{when } i = j \\ 1, & \text{otherwise} \end{cases}$. If |adj A| = |A|², then which of the following statements are correct?

(A) A is a skew symmetric matrix.

(B) A is a non-singular matrix.

(C) A is a square matrix of order 4.

(D) A is a symmetric matrix.

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If $A=\begin{bmatrix}1 & 2 & 2\\2 & 1 & -2\\\alpha & 2 & \beta\end{bmatrix}$ and $AA^T=9I$, where I is the identity matrix of order 3, then $(\beta-\alpha)$ equals:

If a matrix $A=\begin{bmatrix} 3 & -5 & 7 \\ 5 & 2 & 4 \\ -7 & -4 & 9 \end{bmatrix}$ is expressed as the sum of a symmetric matrix P and a skew symmetric matrix Q, then symmetric matrix P will be

Which of the following is NOT correct?

If $A = \begin{bmatrix} 1 & -3 \\ 2 & 0 \end{bmatrix}$, then which of the following statement(s) is/are TRUE?

(A) Matrix A is non-singular

(B) $|3A| = 54$

(C) $|adjA| = 36$

(D) $A^2 = \begin{bmatrix} -5 & -3 \\ 2 & -6 \end{bmatrix}$

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If a matrix has 7 elements, then it can be a

(A) Scalar matrix

(B) Symmetric matrix

(C) Column matrix

(D) Row matrix

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