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Det(A) = 0

so Inverse doesn't exist

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How can you say det =0 ??

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abhishekmehta4u asking 3*3 not 2*2

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The Determinant of an skew symmetric matrix of odd order is always 0.
therefore,A inverse doesn't exist.

Answer 1

Given : A is a $3 \times 3 \ \text{matrix}$

whose elements are $a_{ij} = i^2 - j^2, \  \forall i,j$

$a_{1,1} = 1^2 - 1^2 = 0$

$a_{1,2} = 1^2 - 2^2 = -3$

similarly, 

we'll get, $A = \begin{bmatrix} 0 & -3 & -8\\ 3& 0 &5 \\ 8& -5 & 0 \end{bmatrix}$

$det|A| = 0$

so anwser is D, $A^{-1} \text{doesn't exist}$