Let A be 2 2 matrix Statement -1 : adj ( adj ;A ) = A Statement -… - Vidyadip

MCQ

Let $A$ be $2$$ \times $$2$ matrix

Statement $-1 :$ $adj\left( {adj\;A} \right) = A$

Statement $-2 :$ $\left| {adj\;A} \right| = \left| A \right|$

A
Statement $-1$ is true, Statement $-2$ is false
B
Statement $-1$ is false, Statement $-2$ is true
C
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$
✓
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not acorrect explanation for Statement $-1$

✓

Answer

Correct option: D.

Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not acorrect explanation for Statement $-1$

d
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 acorrect explanation for statement $-1.$

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