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Mathematics

If A=[0110]A = \begin{bmatrix}[r] 0 & 1 \ 1 & 0 \end{bmatrix}, then A2 is equal to:

  1. [1100]\begin{bmatrix}[r] 1 & 1 \ 0 & 0 \end{bmatrix}

  2. [0011]\begin{bmatrix}[r] 0 & 0 \ 1 & 1 \end{bmatrix}

  3. [1001]\begin{bmatrix}[r] 1 & 0 \ 0 & 1 \end{bmatrix}

  4. [0110]\begin{bmatrix}[r] 0 & 1 \ 1 & 0 \end{bmatrix}

Matrices

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Answer

Given,

A=[0110]A = \begin{bmatrix}[r] 0 & 1 \ 1 & 0 \end{bmatrix}

Substituting values we get :

A2=[0110].[0110]=[0×0+1×10×1+1×01×0+0×11×1+0×0]=[0+10+00+01+0]=[1001].A^2 = \begin{bmatrix}[r] 0 & 1 \ 1 & 0 \end{bmatrix} . \begin{bmatrix}[r] 0 & 1 \ 1 & 0 \end{bmatrix}\\[1em] = \begin{bmatrix}[r] 0 \times 0 + 1 \times 1 & 0 \times 1 + 1 \times 0 \ 1 \times 0 + 0 \times 1 & 1 \times 1 + 0 \times 0 \end{bmatrix}\\[1em] = \begin{bmatrix}[r] 0 + 1 & 0 + 0 \ 0 + 0 & 1 + 0 \end{bmatrix}\\[1em] = \begin{bmatrix}[r] 1 & 0 \ 0 & 1 \end{bmatrix}.

Hence, option 3 is the correct option.

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