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.
Answer & explanation
Correct answer: option 3
$A=\left[\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right]$
|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 $\left(\begin{array}{l}A \neq A^T \\ A \neq-A T\end{array}\right) ~~~\begin{array}{l}\text { Not symmetric } \\ \text { Not skew symetric }\end{array}$