Let A be a matrix of size n times n with complex number entries. I_n is the iden

Question

Let A be a matrix of size n times n with complex number entries. I_n is the identity matrix of size n times n. How many of the following assertions are equivalent to the statement: The matrix A is unitary. The inverse of A exists and is equal to A*. The inverse of A exists and is equal to A^T. GEA, applied to SLE Ax = b with any b, proceeds without row interchanges A^-1 exists and is unitary. Let A be a matrix of size n times n with complex number entries. I_n is the identity matrix of size n times n. How many of the following assertions are equivalent to the statement: The matrix A is unitary. Rows of A form an orthogonal basis of C^n AA* = In. A^-1 exists and is unitary. All eigenvalues of A are positive.

Explanation / Answer

For the part a, the answer is (I)and (iv).

(I) and(ii) is the correct answer for part (b).

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