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  4. The number of non-zero diagonal matrices of order 4 satisfying A2 = A is

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

AMUAMU 2015Matrices

Solution:

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