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प्रश्न
Check whether the following matrix is invertible or not:
`[(cos theta, sin theta),(-sin theta, cos theta)]`
Check whether the matrix `[(cos theta, sin theta),(-sin theta, cos theta)]` is invertible or not.
उत्तर
Let A = `[(cos theta, sin theta),(-sin theta, cos theta)]`
Then, |A| = `|(cos theta, sin theta),(-sin theta, cos theta)|`
= cos2θ + sin2θ
= 1 ≠ 0
∴ A is a non-singular matrix.
Hence, A is invertible matrix.
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