Question

Observe the following lists :
List - I List - II
A) If A is a singular 1) ${\left(detA\right)}^{n-1}$
matrix then adj A is
B) If A is a square 2) an idempotent Matrix
matrix then detA=
C) If $A^2$=A then A is 3) Singular
D) If A is square matrix 4) $det{A}^T$
of type n then det (adj A) = 5) a nil potent matrix
The correct match for list - I from list - II is

• A. $A-2,B-3,C-1,D-5$
• B. $A-3,B-4,C-2,D-1$
  
  
• C. $A-4,B-3,C-2,D-5$
  
  
• D. $A-1,B-2,C-3,D-4$
  
  

Answer 1

The correct option is B

$A-3,B-4,C-2,D-1$

a) Given $|A|=0$
$\because adjA=|A|I$
$\therefore adjA=0$
b)Since, $A=A^T$
$\Rightarrow |A|=|A{|}^T$
c) If $A^2=A$ , then A is idempotent matrix.
d) We know that $|adjA|=|A{|}^{n-1}$
Hence, option 'B' is correct.