What does it mean for a matrix to be orthogonal? a. Its determinant is zero. b. It is equal to its negative. c. It has no inverse. d. Its transpose is equal to its inverse.
Question
What does it mean for a matrix to be orthogonal?
a. Its determinant is zero.
b. It is equal to its negative.
c. It has no inverse.
d. Its transpose is equal to its inverse.
Solution
The correct answer is:
d. Its transpose is equal to its inverse.
An orthogonal matrix is a square matrix whose rows and columns are orthogonal unit vectors (i.e., orthonormal vectors), i.e., they are perpendicular and have a length or magnitude of 1. This means that its transpose is equal to its inverse.
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