Question

The number of non-zero diagonal matrices of order $4$ satisfying $A^2=A$ is

• A. 2
• B. 4
• C. 16
• D. 15

Answer 1

Answer: (D)

If $A$ is a diagonal matrix and $A^2=A$
Then, $a_{ii}^2=a_{ii}$ for $i=1,2,3,4\Rightarrow a_{ii}=0$
Hence, total number of $4\times 4$ diagonal matrix
$=2^4=16$
$\therefore$ Number of non-zero diagonal matrix $=16-1=15$