Matrices — Class 12 Maths Solution

exemplar sa SA NCERT,Exemp,Q.no.35,Page 57

Question

Verify that ${A^2} = I$, when $A = \left[ {\begin{array}{cccccccccccccccccccc}0&1&{ - 1}\\4&{ - 3}&4\\3&{ - 3}&4\end{array}} \right]$.

Step-by-step Solution

We have, $A = \left[ {\begin{array}{cccccccccccccccccccc}0&1&{ - 1}\\4&{ - 3}&4\\3&{ - 3}&4\end{array}} \right]$

$\therefore$ ${A^2} = \left[ {\begin{array}{cccccccccccccccccccc}0&1&{ - 1}\\4&{ - 3}&4\\3&{ - 3}&4\end{array}} \right] \cdot \left[ {\begin{array}{cccccccccccccccccccc}0&1&{ - 1}\\4&{ - 3}&4\\3&{ - 3}&4\end{array}} \right]$

$= \left[ {\begin{array}{llllllllllllllllllll}1&0&0\\0&1&0\\0&0&1\end{array}} \right] = I$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Matrices. Curated by Sachin Sharma. Free for all students.