MAT2611 Assignment 08 (Accurate Solutions) Due 25 July 2025

MAT2611 Assignment 08 Solutions
Student Name: [Your Name]
Due: Friday, 25 July 2025


Problem 1
Problem Statement
(a) Show that if A is an orthogonal matrix, then AT is also an orthogonal matrix.
(b) Show that if A and B are orthogonal matrices, then AB is also an
orthogonal matrix.
—

Part (a)
Step 1. Recall the definition: A is orthogonal if AT A = I.
Step 2. To prove AT is orthogonal, check if:

(AT )T AT = I.
Since (AT )T = A, we have:

AAT = I.
Step 3. Thus, AT satisfies the orthogonality condition.
Final Answer. If A is orthogonal, then AT is also orthogonal because:

AT A = I =⇒ AAT = I.
—

Part (b)
Step 1. Given A and B are orthogonal:

AT A = I, B T B = I.
Step 2. Check if AB is orthogonal:

(AB)T (AB) = B T AT AB.
Step 3. Since AT A = I, we get:


1