If $[m\ n]\left[ {\begin{array}{*{20}{c}}m\\n\end{array}} \right] = [25]$ and $m< n$, then $(m, n) =$

If $2X – \left[ {\begin{array}{*{20}{c}}1&2\\7&4\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}3&2\\0&{ – 2}\end{array}} \right]$, then $X$  is equal to

If $A\, = \,\left[ {\begin{array}{*{20}{c}}
{{e^t}}&{{e^{ – t}}\,\cos \,t}&{{e^{ – t}}\,\sin \,t}\\
{{e^t}}&{ – {e^{ – t}}\,\cos \, – {e^{ – t}}\,\sin \,t}&{ – {e^{ – t}}\,\sin \,t\, + \,{e^{ – t}}\,\cos \,t}\\
{{e^t}}&{2{e^{ – t}}\,\sin \,t}&{2{e^{ – t}}\,\cos \,t}
\end{array}} \right]$ Then $A$ is

If $A = \left[ {\begin{array}{*{20}{c}}1&{ – 1}\\2&{ – 1}\end{array}} \right],\,\,B = \left[ {\begin{array}{*{20}{c}}a&1\\b&{ – 1}\end{array}} \right]$ and ${(A + B)^2} = {A^2} + {B^2}$, then the value of $a$ and $b$ are

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 $AB$