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 $-1 :$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 :
- [AIEEE 2011]
- A
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$
- B
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$
- C
Statement $-1$ is false, Statement $-2$ is true
- D
Statement $-1$ is true, Statement $-2$ is false
Similar Questions
$\left| {\,\begin{array}{*{20}{c}}{1 + i}&{1 - i}&i\\{1 - i}&i&{1 + i}\\i&{1 + i}&{1 - i}\end{array}\,} \right| = $
$\left| {\,\begin{array}{*{20}{c}}{1 + i}&{1 - i}&i\\{1 - i}&i&{1 + i}\\i&{1 + i}&{1 - i}\end{array}\,} \right| = $
The remainder when the determinant $\left|\begin{array}{lll} 2014^{2014} & 2015^{2015} & 2016^{2016} \\ 2017^{2017} & 2018^{2018} & 2019^{2019} \\ 2020^{2020} & 2021^{2021} & 2022^{2022} \end{array}\right|$ is divided by $5$ is
The remainder when the determinant $\left|\begin{array}{lll} 2014^{2014} & 2015^{2015} & 2016^{2016} \\ 2017^{2017} & 2018^{2018} & 2019^{2019} \\ 2020^{2020} & 2021^{2021} & 2022^{2022} \end{array}\right|$ is divided by $5$ is
- [KVPY 2015]
Evaluate $\left|\begin{array}{rr}2 & 4 \\ -1 & 2\end{array}\right|$
Evaluate $\left|\begin{array}{rr}2 & 4 \\ -1 & 2\end{array}\right|$
The system of equations $kx + y + z =1$ $x + ky + z = k$ and $x + y + zk = k ^{2}$ has no solution if $k$ is equal to
The system of equations $kx + y + z =1$ $x + ky + z = k$ and $x + y + zk = k ^{2}$ has no solution if $k$ is equal to
- [JEE MAIN 2021]
Let $\lambda, \mu \in R$. If the system of equations
$ 3 x+5 y+\lambda z=3 $
$ 7 x+11 y-9 z=2 $
$ 97 x+155 y-189 z=\mu$
has infinitely many solutions, then $\mu+2 \lambda$ is equal to :
Let $\lambda, \mu \in R$. If the system of equations
$ 3 x+5 y+\lambda z=3 $
$ 7 x+11 y-9 z=2 $
$ 97 x+155 y-189 z=\mu$
has infinitely many solutions, then $\mu+2 \lambda$ is equal to :
- [JEE MAIN 2024]