If a matrix $A =\begin{bmatrix}5&-8\\-3&5\end{bmatrix}$ then which of the following is/are TRUE?
(A) $|A| = 1$
(B) A is a singular matrix.
(C) $-2A=\begin{bmatrix}10&-16\\-6&10\end{bmatrix}$
(D) $AI =\begin{bmatrix}5&0\\0&5\end{bmatrix}$, I is an identity matrix of order 2.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) only
$|A|=5\cdot5-(-8)(-3)=25-24=1$
$A$ is not singular (determinant $\neq 0$)
$-2A=\begin{pmatrix}-10 & 16\\ 6 & -10\end{pmatrix}\neq\begin{pmatrix}10 & -16\\ -6 & 10\end{pmatrix}$
$AI=A\neq\begin{pmatrix}5 & 0\\ 0 & 5\end{pmatrix}$
Only (A) is true.