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Evaluation of a Determinant

If I is uni...

Question

If $I$ is unit matrix of order $10$ , then the determinant of $I$ is equal to

10

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1

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\frac{1}{10}

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9

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Solution

The correct option is A $1$
$I = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$ is order $10$
$| I | = 1 ⎛ ⎜ ⎝ ∴ I_{1} = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}], | I_{1} | = 1 I_{2} = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦, | I_{2} | = 1 ⎞ ⎟ ⎠$

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