Operations on Matrices

The matrix $X$ is such that  $2A+B+X=0$ , where $A=\left[\begin{array}{cc}-1& 2\\ 3& 4\end{array}\right]$ and $B=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]$. The matrix $X$ is:

If $\mathrm{A}=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$, for ${\mathrm{A}}^6=\mathrm{\lambda A}$, then $\lambda =$_____

$\mathrm{P} \mathrm{and} \mathrm{Q}$ are matrices such that both $\left(\mathrm{P}+\mathrm{Q}\right)$ and $\left(\mathrm{PQ}\right)$ are defined.

Which of the following is true about $\mathrm{P} \mathrm{and} \mathrm{Q}$?

If matrix $\left[\begin{array}{cc}a+b& 2\\ 5& ab\end{array}\right]=\left[\begin{array}{cc}6& 2\\ 5& 8\end{array}\right]$, find the values of $a$ and $b$.

Let $A=\left[\begin{array}{cc}3& 4\\ 1& -2\end{array}\right]$ and let $AB=\left[\begin{array}{cc}-5& 4\\ 5& -13\end{array}\right]$. Then $\left|B^T\right|=$

If $A$ and $B$ are two matrices such that $AB=A \& BA=B$, then number of elements in the set $\left\{A=\left[\begin{array}{cc}a& b\\ 0& d\end{array}\right]: a,b,d\in \left\{-1,0,1\right\}\right\}$ is

Which one is the condition for Multiplication of Two Matrices?

If $A=\left[\begin{array}{cc}1& 5\\ 2& 3\end{array}\right], B=\left[\begin{array}{cc}-1& 1\\ 5& -3\end{array}\right]$  and $C=\left[\begin{array}{cc}3& 1\\ 2& 1\end{array}\right]$then $\left(AB\right)C=A\left(BC\right)$, why? 

Which one is the property of multiplication of matix.

If $\mathrm{I}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$​. Then $-\mathrm{I}$ is

For the matrices of the order $3\times 3$ and $2\times 2$ are to be added or not?

If $A$ is a square matrix such that $A^2=A$, then ${\left(I+A\right)}^3-7A$ is

If $A=\left[\begin{array}{cc}5& 2016\\ 1& 403\end{array}\right]$, then the value of $det\left(A^{2015}-5A^{2014}\right)=$________

If $f\left(x\right)=x^2+4x-3$ and $A=\left[\begin{array}{cc}1& 2\\ 4& -3\end{array}\right]$, then find $f\left(A\right)$.

If $A=\left[\begin{array}{ll}2& 4\\ 6& 8\end{array}\right]$, then find $A^2$.

If $A=\left[\begin{array}{ll}1& 3\\ 5& 7\end{array}\right]$, then find $A^2$.

If $A=\left[\begin{array}{ll}1& 1\\ 2& 2\end{array}\right]$, then find $A^2$.

If $A=\left[\begin{array}{ll}1& 3\\ 2& 4\end{array}\right]$, then find $A^2$.