Question

If A=[cos⁡αsin⁡α−sin⁡αcos⁡α] then AAT is equal to: (where AT is the transpose of A)

• A. (A) Null matrix
• B. (B) Identify matrix
• C. (C) A
• D. (D) -A

Answer 1

Answer: (B)

(B) Identify matrix

Answer 2

Explanation:
Given,A=[cos⁡αsin⁡α−sin⁡αcos⁡α]The transpose of matrix A is given by,AT=[cos⁡α−sin⁡αsin⁡αcos⁡α]Now,AAT=[cos⁡αsin⁡α−sin⁡αcos⁡α]×[cos⁡α−sin⁡αsin⁡αcos⁡α]⇒AAT=[cos2⁡α+sin2⁡α−cos⁡αsin⁡α+cos⁡αsin⁡α−cos⁡αsin⁡α+cos⁡αsin⁡αsin2⁡α+cos2⁡α]⇒AAT=[1001]⇒AAT=ISo, AAT is a identify matrix.Hence, the correct option is (B).