Let A be a square matrix such that {a_{ij}} ∈ left{ { - 1,0,1} right}∀,, i,j and it

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3 and 4 .Determinants and Matrices

hard

Let $A$ be a square matrix such that ${a_{ij}} \in \left\{ { - 1,0,1} \right\}\forall\,\, i,j$ and it has only one non-zero entry in each row as well as in each column, then

A

$A$ can be singular matrix

B

$A$ must be skew symmetric

C

$A$ must be symmetric

D

$A$ must be orthogonal

Solution

As $AA^T = I_n\, \Rightarrow \, A$ is orthogonal

$\Rightarrow detA \neq 0\, \Rightarrow\, A$ is non-singular

Standard 12

Mathematics

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