The product of two Unitary matrices is a ... matrixa)Unitb)Unitaryc)Orthogonald)None of the aboveCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Yes C is correct answer becoz A inverse =AStar by the definition of unitary matrix.

Answer

Product of Two Unitary Matrices

Unitary matrices are square matrices whose conjugate transpose is equal to their inverse. When two unitary matrices are multiplied together, the resulting matrix may or may not be unitary.

Explanation

- When two unitary matrices are multiplied together, the result is not necessarily a unitary matrix.
- The product of two unitary matrices may be an orthogonal matrix.
- An orthogonal matrix is a square matrix whose transpose is equal to its inverse.
- Therefore, the product of two unitary matrices is an orthogonal matrix, not necessarily a unitary matrix.

Conclusion

In conclusion, the product of two unitary matrices is an orthogonal matrix. While unitary matrices have the property of having an inverse equal to their conjugate transpose, the result of multiplying two unitary matrices may not maintain this property and instead result in an orthogonal matrix.

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