A square matrix A is said to be ... if AAT = Ia)Idempotentb)Orthogonalc)Unitaryd)Hermitian MatrixCorrect answer is option 'B'. Can you explain this answer?

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Answer

Orthogonal Matrix Explanation:
An orthogonal matrix is a square matrix whose transpose is equal to its inverse. In other words, for a matrix A to be orthogonal, it must satisfy the condition: A^T * A = I, where I is the identity matrix.

Orthogonal Matrix Properties:
- Orthogonal matrices preserve the length of vectors and the angles between vectors.
- The columns of an orthogonal matrix form an orthonormal set of vectors.
- The determinant of an orthogonal matrix is either 1 or -1.

Relation to the Given Matrix A:
In the given scenario, the matrix A is said to be orthogonal if A^T * A = I. This implies that the matrix A is orthogonal when its transpose multiplied by itself results in the identity matrix.
Therefore, in the context of the question, the correct answer is option 'B - Orthogonal'. A matrix satisfying the condition A^T * A = I is an orthogonal matrix.
By understanding the properties and characteristics of orthogonal matrices, one can easily identify and determine whether a given square matrix is orthogonal or not based on the defined criteria.

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