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If I3 denotes...

Question

If I₃ denotes identity matrix of order 3 × 3, write the value of its determinant.

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Solution

In an identity matrix, all the diagonal elements are 1 and rest of the elements are 0.
Here,

$I_{3} = |1 0 0 0 1 0 0 0 1| = 1 \times |1 0 0 1| [Expanding along C_{1}] = 1 \Rightarrow I_{3} = 1$

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