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JEE Main 2018
Matrices & Determinants
Matrices and Determinants
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Question

Let AA be a 2×2\,2 \times 2 matrix Statement - 1 : adj(adjA)=Aadj\left( {adj\,A} \right) = A Statement - 2 : adjA=A\left| {adj\,A} \right| = \left| A \right|

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Solution

We know that adj(adjA)=AdjA21\left| {adj\left( {adj\,\,A} \right)} \right| = {\left| {Adj\,\,A} \right|^{2 - 1}}b \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\, =A21=A\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\left| A \right|^{2 - 1}} = \left| A \right| \therefore \,\,\,\,\,\, Both the statements are true and statement 2-2 is a correct explanation for statement - 1.1.

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