Question

State True or False for the statement below:

$|A^{-1}|\ne |A{|}^{-1}$, where $A$ is a non-singular matrix.

• A. False
• B. True

Answer 1

The correct option is A False

Answer: b

We know, $A{A}^{-1}=I$,

where $A$ is a non-singular matrix.

Take determinant both sides

$\Rightarrow |A{A}^{-1}|=|I|$

$\Rightarrow |A||A^{-1}|=1$

$(\because |AB|=|A||B|\text{\&}|I|=1)$

$\Rightarrow |A^{-1}|=\frac{1}{|A|}=(|A|{)}^{-1}$

Hence, the given statement is false.