If $A = [1\,\,2\,{\rm{ }}3]$and $B = \left[ {\begin{array}{*{20}{c}}{ - 5}&4&0\\0&2&{ - 1}\\1&{ - 3}&2\end{array}} \right]$, then $AB = $

Suppose $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ is a real matrix with non-zero entries, $\alpha d-b c=0$ and $A^2=A$. Then, $a + d$ equals

Let $A$ and $B$ be real matrices of the form $\left[ {\begin{array}{*{20}{c}}
\alpha &0\\
0&\beta 
\end{array}} \right]$ and $\left[ {\begin{array}{*{20}{c}}
0&\gamma \\
\delta &0
\end{array}} \right]$, respectively

Statement $1$ : $AB - BA$ is always an invertible matrix

Statement $2$ : $AB -BA$ is never an identity matrix

If a matrix has $8$ elements, what are the possible orders it can have ?

Let $A=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right], B=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right], C=\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right]$

Find $BA$

The matrix $\left[ {\begin{array}{*{20}{c}}2&\lambda &{ - 4}\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}} \right]$is non singular, if