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Statement $-1 :$Determinant of a skew-symmetric matrix of order $3$ is zero
Statement $-2 :$ For any matrix $A,$ $\det \left( {{A^T}} \right) = {\rm{det}}\left( A \right)$ and $\det \left( { - A} \right) = - {\rm{det}}\left( A \right)$ Where $\det \left( A \right) = A$. Then :
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$
Statement $-1$ is false, Statement $-2$ is true
Statement $-1$ is true, Statement $-2$ is false
Solution
Statement $- 1:$ Determinant of a skew sysmmetric matrix of odd order is zero Statement $-$ $2: \operatorname{det}\left(A^{T}\right)=\operatorname{det}(A)$ $\operatorname{det}(-A)=(-1)^{n} \operatorname{det}(A)$ where $\mathrm{A}$ is an $\times$ norder matrix
