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If a = ⎡ ⎢ ⎣ − 1 0 0 0 − 1 0 0 0 − 1 ⎤ ⎥ ⎦ , Find A2. - Mathematics

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प्रश्न

 If \[A = \begin{bmatrix}- 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1\end{bmatrix}\] , find A2.
 

 

योग

उत्तर

\[Here, \] 

\[ A^2 = AA\] 

\[ \Rightarrow A^2 = \begin{bmatrix}- 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1\end{bmatrix}\begin{bmatrix}- 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1\end{bmatrix}\] 

\[ \Rightarrow A^2 = \begin{bmatrix}1 + 0 + 0 & 0 + 0 + 0 & 0 + 0 + 0 \\ 0 + 0 + 0 & 0 + 1 + 0 & 0 + 0 + 0 \\ 0 + 0 + 0 & 0 + 0 + 0 & 0 + 0 + 1\end{bmatrix}\] 

\[ \Rightarrow A^2 = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}\]

 

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अध्याय 5: Algebra of Matrices - Exercise 5.6 [पृष्ठ ६२]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 5 Algebra of Matrices
Exercise 5.6 | Q 13 | पृष्ठ ६२

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