Embibe Experts Solutions for Chapter: Matrices and Determinants, Exercise 1: EXERCISE-1

Let a determinant is given by$A=\left[\begin{array}{c}\begin{array}{lll}a& b& c\\ p& q& r\\ x& y& z\end{array}\end{array}\right]$ and suppose determinant $A=6$. If $B=\left[\begin{array}{c}\begin{array}{ccc}p+x& q+y& r+z\\ a+x& b+y& c+z\\ a+p& b+q& c+r\end{array}\end{array}\right]$

If $A=\left[\begin{array}{ccc}a& 0& 0\\ 0& a& 0\\ 0& 0& a\end{array}\right]$, then $\left|A\right|\left|AdjA\right|$ is equal to -

If $A=\left[\begin{array}{cc}2& 3\\ 5& -2\end{array}\right]$, then $19A^{-1}$ is equal to -

If $A$ and $B$ are square matrices of same order, then which of the following is correct -

Let three matrices $A=\left[\begin{array}{ll}2& 1\\ 4& 1\end{array}\right]; B=\left[\begin{array}{ll}3& 4\\ 2& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}3& -4\\ -2& 3\end{array}\right]$ then

$t_{\mathrm{r}}\left(\mathrm{A}\right)+t_{\mathrm{r}}\left(\frac{ABC}{2}\right)+t_{\mathrm{r}}\left(\frac{A(BC{)}^2}{4}\right)+{\mathrm{t}}_{\mathrm{r}}\left(\frac{A(BC{)}^3}{8}\right)+\dots \dots +\infty =$

If ${\left[\begin{array}{ll}1& 1\\ 0& 1\end{array}\right]}^{-1}{\left[\begin{array}{ll}1& 2\\ 0& 1\end{array}\right]}^{-1}{\left[\begin{array}{ll}1& 3\\ 0& 1\end{array}\right]}^{-1}\dots \dots ··{\left[\begin{array}{cc}1& 100\\ 0& 1\end{array}\right]}^{-1}=\left[\begin{array}{ll}1& \mathrm{a}\\ \mathrm{b}& 1\end{array}\right]$, then $a+b=$

Let $A^{-1}=BC$ then the value of $\mathit{tr}(ABC+BCA+CAB)$ is equal to (where the order of matrices  $A$, $B$, $C$ is $3$ &  $tr\left(A\right)$is sum of diagonal elements $A$)

If  $A$ is a non singular square matrix where $B\mathit{=}{A}^{\mathit{T}}$ & $A\mathit{+}{B}^2=I$, such that $A^3+I\mathit{=}kA$ then $k$is equal to