Tag: applications of matrices and determinants

Matrices $A$ and $B$ will be inverse of each other only if

 Let A$= \left[\begin{array}{lll}1 & 0 & 0\2 & 1 & 0\3 & 2 & 1\end{array}\right]$.If $\mathrm{u _1}$ and $\mathrm{u} _{2}$ are column matrices such that  $\mathrm{Au _{1}}=\left[\begin{array}{l}1\0\0\end{array}\right]$ and  $\mathrm{Au _{2}}=\left[\begin{array}{l}0\1\0\end{array}\right]$ then $\mathrm{u _{1}+u _{2}}$ is equal to:

If a $3\times 3$ matrix $A$ has its inverse equal to $A$, then ${A}^{2}$ is equal to

If $A$ is an $3\times 3$ non -singular matrix that $AA'=A'A$ and $B=A^{-1}A'$,then $BB'$ equal ?

 ${( -A )}^{ -1 }$ is always equal to (where $A$ is $nth$ order square matrix)

If $A\left( \alpha ,\beta  \right) =\left[ \begin{matrix} \cos { \alpha  }  & \sin { \alpha  }  & 0 \ -\sin { \alpha  }  & \cos { \alpha  }  & 0 \ 0 & 0 & { e }^{ \beta  } \end{matrix} \right]$, then $A{ \left( \alpha ,\beta  \right)  }^{ -1 }$ is equal to 

Let $a, b, c$ are non real number satisfying equation $x^{5}=1$ and $S$ be the set of all non-invertible matrices of the from $\begin{bmatrix} 1 & a & b \ w & 1 & c \ { w }^{ 2 } & w & 1 \end{bmatrix}$ where $w={ e }^{ \dfrac { 12\pi  }{ 5 }  }$. The number of distinct matrices in set $S$ is 

If A is an invertible matrix, then det $\displaystyle :\left ( A^{-1} \right )$ is equal to

If $\displaystyle [A]\neq 0 $ then which of the following is not true?

Which of the following matrix is inverse of itself