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Mathematics

If matrix P = [−204−3]\begin{bmatrix}[r] -2 & 0 \ 4 & -3 \end{bmatrix}, then P2 is :

  1. [40−209]\begin{bmatrix}[r] 4 & 0 \ -20 & 9 \end{bmatrix}

  2. [40−20−9]\begin{bmatrix}[r] 4 & 0 \ -20 & -9 \end{bmatrix}

  3. [−40−209]\begin{bmatrix}[r] -4 & 0 \ -20 & 9 \end{bmatrix}

  4. [4020−9]\begin{bmatrix}[r] 4 & 0 \ 20 & -9 \end{bmatrix}

Matrices

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Answer

Given,

P = [−204−3]\begin{bmatrix}[r] -2 & 0 \ 4 & -3 \end{bmatrix}

Evaluating :

⇒P2=[−204−3][−204−3]=[−2×−2+0×4−2×0+0×−34×−2+−3×44×0+−3×−3]=[4+00+0−8−120+9]=[40−209].\Rightarrow P^2 = \begin{bmatrix}[r] -2 & 0 \ 4 & -3 \end{bmatrix}\begin{bmatrix}[r] -2 & 0 \ 4 & -3 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] -2 \times -2 + 0 \times 4 & -2 \times 0 + 0 \times -3 \ 4 \times -2 + -3 \times 4 & 4 \times 0 + -3 \times -3 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 4 + 0 & 0 + 0 \ -8 - 12 & 0 + 9 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 4 & 0 \ -20 & 9 \end{bmatrix}.

Hence, Option 1 is the correct option.

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