If $A=\left[\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right]$, then which of the following statements are correct?

A. A is a square matrix
B. A^-1 exists
C. A is a symmetric matrix
D. |A| = 19
E. A is a null matrix

Choose the correct answer from the options given below.

A, B, D only

$A=\left[\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right]$

|A| = 2 × 5 -(-3) (3) = 10 +9

|A| = 19  ⇒  |A| ≠ 0

⇒ A^-1 exist

$A^T=\left[\begin{array}{cc}2 & 3 \\ -3 & 5\end{array}\right]$

so $\left(\begin{array}{l}A \neq A^T \\ A \neq-A T\end{array}\right)  ~~~\begin{array}{l}\text { Not symmetric } \\ \text { Not skew symetric }\end{array}$