The correct answer is a. A matrix is considered orthogonal if its transpose is equal to its inverse. This means that if you flip the matrix over its main diagonal (from top-left to bottom-right) to get the transpose, and then calculate the inverse of the original matrix, the two results will be the same.

Option b is incorrect because a matrix with a determinant of zero is known as a singular or degenerate matrix, not an orthogonal matrix.

Option c is incorrect because a matrix being equal to its negative would imply that all elements in the matrix are zero, which is not a requirement for a matrix to be orthogonal.

Option d is incorrect because orthogonal matrices do have inverses. In fact, the inverse of an orthogonal matrix is its transpose, as stated in option a.

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The correct answer is a. A matrix is considered orthogonal if its transpose is equal to its inverse. This means that if you flip the matrix over its main diagonal (from top-left to bottom-right) to get the transpose, and then calculate the inverse of the original matrix, the two results will be the same.

Option b is incorrect because a matrix with a determinant of zero is known as a singular or degenerate matrix, not an orthogonal matrix.

Option c is incorrect because a matrix being equal to its negative would imply that all elements in the matrix are zero, which is not a requirement for a matrix to be orthogonal.

Option d is incorrect because orthogonal matrices do have inverses. In fact, the inverse of an orthogonal matrix is its transpose, as stated in option a.

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The correct answer is a. A matrix is considered orthogonal if its transpose is equal to its inverse. This means that if you flip the matrix over its main diagonal (from top-left to bottom-right) to get the transpose, and then calculate the inverse of the original matrix, the two results will be the same.

Option b is incorrect because a matrix with a determinant of zero is known as a singular or degenerate matrix, not an orthogonal matrix.

Option c is incorrect because a matrix being equal to its negative would imply that all elements in the matrix are zero, which is not a requirement for a matrix to be orthogonal.

Option d is incorrect because orthogonal matrices do have inverses. In fact, the inverse of an orthogonal matrix is its transpose, as stated in option a.

What does it mean for a matrix to be orthogonal?a.Its transpose is equal to its inverse.b.Its determinant is zero.c.It is equal to its negative.d.It has no inverse.

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