Maths

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}True.\\ LetA={\left[a_{ij}\right]}_{m*n}andB={\left[b_{ij}\right]}_{p*q}\\ ABisdefinedwhenn=P\\ \therefore OrderofAB=m*q\\ \Rightarrow Orderof{\left(AB\right)}^{\text{'}}=q*m\\ Orderof{B}^{\text{'}}isq*pandorderof{A}^{\text{'}}isn*m\\ \therefore B^{\text{'}}{A}^{\text{'}}isdefinedwhenP=n\\ andtheorderof{B}^{\text{'}}{A}^{\text{'}}isq*m\\ Hence,Orderof{\left(AB\right)}^{\text{'}}=Orderof{B}^{\text{'}}{A}^{\text{'}}i.e.,q*m.\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}False.\\ Since{\left(AB\right)}^{\text{'}}=B^{\text{'}}{A}^{\text{'}}.\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}True.\\ LetA,B,andCbethreematricesofthesameorder.\\ Giventhat{A}^{\text{'}}=A,B^{\text{'}}=B,and{C}^{\text{'}}=C\\ LetP=A+B+C\\ \Rightarrow P^{\text{'}}={\left(A+B+C\right)}^{\text{'}}\\ =A^{\text{'}}+B^{\text{'}}+C^{\text{'}}=A+B+C=P\\ So,A+B+Cisalsoasymmetricmatrix.\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}False.\\ FortwosquarematricesAandB,AB=BAisnotalwaystrue.\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}False.\\ Sinceforanytwonon-zeromatricesAandB,wemaygetAB=0.\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}False.\\ Sincesubtractionsofanytwomatricesofthesameorderisnotcommutativei.e.,A-B\ne B-A\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}True.\\ IfAandBaresquarematricesofthentheiradditioniscommutativei.e.,A+B=B+A\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}False.\\ Thetwomatricesaresaidtobeequaliftheircorrespondingelementsaresame.\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}False.\\ Since,inanidentitymatrixalltheelementsofprincipaldiagonalareunityrestarezero.\\ e.g.,A=\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]=I_3\end{array}$