If \[A = \begin{bmatrix}4 & - 1 & - 4 \\ 3 & 0 & - 4 \\ 3 & - 1 & - 3\end{bmatrix}\] , Show that A2 = I3.

Here, `A^2`=AA ⇒` A^2 =[[4 -1 -4],[3 0 -4],[3 -1 -3]]` `[[4 -1 -4],[3 0 -4],[3 -1 -3]]` `⇒ A^2=[[16-3-12 -4+0+4 -16+4+12],[12+0-12 -3+0+4 -12+0+12],[12-3-9 -3+0+3 -12+4+9]]` `⇒ A^2=` `[[1 0 0],[0 1 0],[0 0 1]]` &there4; `A^2=I_3`

If A=`[[4 -1 -4],[3 0 -4],[3 -1 -3]]` Show That A2 = I3. - Mathematics

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If $A = [\begin{matrix} 4 & - 1 & - 4 \\ 3 & 0 & - 4 \\ 3 & - 1 & - 3 \end{matrix}]$ , Show that A² = I₃.

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उत्तर

Here,

$A^{2}$ =AA

⇒ $A^{2} = [\begin{matrix} 4 - 1 - 4 \\ 3 0 - 4 \\ 3 - 1 - 3 \end{matrix}]$ $[\begin{matrix} 4 - 1 - 4 \\ 3 0 - 4 \\ 3 - 1 - 3 \end{matrix}]$

$\Rightarrow A^{2} = [\begin{matrix} 16 - 3 - 12 - 4 + 0 + 4 - 16 + 4 + 12 \\ 12 + 0 - 12 - 3 + 0 + 4 - 12 + 0 + 12 \\ 12 - 3 - 9 - 3 + 0 + 3 - 12 + 4 + 9 \end{matrix}]$

$\Rightarrow A^{2} =$ $[\begin{matrix} 1 0 0 \\ 0 1 0 \\ 0 0 1 \end{matrix}]$

∴ $A^{2} = I_{3}$

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अध्याय 5: Algebra of Matrices - Exercise 5.3 [पृष्ठ ४३]

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अध्याय 5 Algebra of Matrices
Exercise 5.3 | Q 23 | पृष्ठ ४३

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