Determinants — Class 12 Maths Solution

Opton b is corect

When A is an invertible matrix of order 2, $A{A^{ - 1}} = {I_2} = {A^{ - 1}}A,$

where ${I_2}$ is identity matrix of order 2.
$\Rightarrow$ $\det (A{A^{ - 1}}) = \det I \Rightarrow \det A.\det ({A^{ - 1}}) = 1$

$\Rightarrow$ $\det ({A^{ - 1}}) = \cfrac{1}{{\det \;A}},\det A \ne 0$

\node[draw=red, rectangle, ultra thick, rounded corners, inner sep=10pt, fill =yellow]{