Let A be a \[\,2 \times 2\] matrix
Statement - 1 : \[adj\left( {adj\,A} \right) = A\]
Statement - 2 :\[\left| {adj\,A} \right| = \left| A \right|\]
Solutions · 1
Official solution
We know that \[\left| {adj\left( {adj\,\,A} \right)} \right| = {\left| {Adj\,\,A} \right|^{2 - 1}}\]b
\[\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\] \[\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\] \[\,\,\,\,\,\,\,\,\,\,\,\,\] \[\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\left| A \right|^{2 - 1}} = \left| A \right|\]
\[\therefore\] \[\,\,\,\,\,\,\] Both the statements are true and statement −2 is a correct explanation for statement - 1.