3 and 4 .Determinants and Matrices
easy

જો $A = \left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]$, તો $|{A^2} - 2A|= . . . $

A

$5$

B

$25$

C

$-5$

D

$-25$

Solution

(b) $A = \left| {\,\begin{array}{*{20}{c}}
1&3\\
2&1
\end{array}\,} \right| $

$\therefore$ ${A^2} = \left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]\, = \,\left[ {\begin{array}{*{20}{c}}7&6\\4&7\end{array}} \right]$

and ${A^2} – 2A = \left[ {\begin{array}{*{20}{c}}5&0\\0&5\end{array}} \right]\,,{\rm{det }}({A^2} – 2A) = \left| {\,\begin{array}{*{20}{c}}5&0\\0&5\end{array}\,} \right| = 25$.

Standard 12
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.