Matrices and Determinants
Orthogonal Matrices
Premium Question
Grade 12
Question:
A square matrix $A$ is said to be orthogonal if it satisfies:
(1) $A^{-1} = A$
(2) $A^T = A$
(3) $A^{-1} = A^T$
(4) $A^2 = I$
Step-by-Step Solution
Key Concept: Recall the defining relation of an orthogonal matrix — it links the inverse of the matrix to a simple transformation of the matrix itself that is much easier to compute than a true inverse.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)