A=begin{bmatrix} 1 & 0 & 1 0 & 1 & 1 0 & 1 | vedclass

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(B) આપેલ છે,$A = \begin{bmatrix} 1 & 0 & 1 \ 0 & 1 & 1 \ 0 & 1 & 0 \end{bmatrix}$.પ્રથમ,$A^2 = A 	imes A = \begin{bmatrix} 1 & 0 & 1 \ 0 & 1 & 1 \

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$-A^{-1}$

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(B) આપેલ છે,$A = \begin{bmatrix} 1 & 0 & 1 \ 0 & 1 & 1 \ 0 & 1 & 0 \end{bmatrix}$.પ્રથમ,$A^2 = A 	imes A = \begin{bmatrix} 1 & 0 & 1 \ 0 & 1 & 1 \ 0 & 1 & 0 \end{bmatrix} \begin{bmatrix} 1 & 0 & 1 \ 0 & 1 & 1 \ 0 & 1 & 0 \end{bmatrix} = \begin{bmatrix} 1 & 1 & 1 \ 0 & 2 & 1 \ 0 & 1 & 1 \end{bmatrix}$ શોધો.હવે,$A^2 - 2A = \begin{bmatrix} 1 & 1 & 1 \ 0 & 2 & 1 \ 0 & 1 & 1 \end{bmatrix} - 2 \begin{bmatrix} 1 & 0 & 1 \ 0 & 1 & 1 \ 0 & 1 & 0 \end{bmatrix} = \begin{bmatrix} 1 & 1 & 1 \ 0 & 2 & 1 \ 0 & 1 & 1 \end{bmatrix} - \begin{bmatrix} 2 & 0 & 2 \ 0 & 2 & 2 \ 0 & 2 & 0 \end{bmatrix} = \begin{bmatrix} -1 & 1 & -1 \ 0 & 0 & -1 \ 0 & -1 & 1 \end{bmatrix}$.આગળ,$|A| = 1(0-1) - 0 + 1(0-0) = -1$ શોધો.સહ-અવયવ શ્રેણિક $C$ માટે $C_{ij} = (-1)^{i+j} M_{ij}$ છે.$C_{11} = -1, C_{12} = 0, C_{13} = 0$.$C_{21} = 1, C_{22} = 0, C_{23} = -1$.$C_{31} = -1, C_{32} = -1, C_{33} = 1$.$adj(A) = C^T = \begin{bmatrix} -1 & 1 & -1 \ 0 & 0 & -1 \ 0 & -1 & 1 \end{bmatrix}$.$A^{-1} = \frac{1}{|A|} adj(A) = \frac{1}{-1} \begin{bmatrix} -1 & 1 & -1 \ 0 & 0 & -1 \ 0 & -1 & 1 \end{bmatrix} = \begin{bmatrix} 1 & -1 & 1 \ 0 & 0 & 1 \ 0 & 1 & -1 \end{bmatrix}$.$A^2 - 2A = \begin{bmatrix} -1 & 1 & -1 \ 0 & 0 & -1 \ 0 & -1 & 1 \end{bmatrix}$ અને $-A^{-1} = - \begin{bmatrix} 1 & -1 & 1 \ 0 & 0 & 1 \ 0 & 1 & -1 \end{bmatrix} = \begin{bmatrix} -1 & 1 & -1 \ 0 & 0 & -1 \ 0 & -1 & 1 \end{bmatrix}$ ની સરખામણી કરતા.આમ,$A^2 - 2A = -A^{-1}$.

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

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$\Delta ABC$ માં,જો $\left| \begin{array}{ccc} 1 & a & b \\ 1 & c & a \\ 1 & b & c \end{array} \right| = 0$ હોય,તો $\sin^2 A + \sin^2 B + \sin^2 C = $

જો $A = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix}$ હોય,તો સાબિત કરો કે $A^{3} - 6A^{2} + 7A + 2I = 0$.

જો $D_1$ અને $D_2$ બે $3 \times 3$ વિકર્ણ શ્રેણિકો (diagonal matrices) હોય,તો

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