NCERT Solutions for CBSE Class 12th Mathematics, Chapter 3: Matrices are available here. In this article, you will get detailed explanations of exercise 3.3 (from question number 7 to question number 12). These questions are related to operations on concepts related to: Transpose of a Matrix, Properties of transpose of the matrices, Symmetric and Skew Symmetric Matrices. These questions are also important for Class 12 Maths board exam 2018 and other engineering entrance exams like JEE Mains, JEE Advanced etc.
NCERT Solutions for CBSE Class 12th Maths, Chapter 3: Matrices (Exercise 3.3) from question number 7 to 12 are given below:
Question 11: If A, B are symmetric matrices of same order, then AB – BA is a
(A) Skew symmetric matrix
(B) Symmetric matrix
(C) Zero matrix
(D) Identity matrix
A and B are symmetric matrices,
A’ = A
B’ = B
(AB ‒ BA)’ = (AB)’ ‒ (BA)’ = B’A’ ‒ A’B’ = BA ‒ AB = ‒ (AB ‒ BA)
Therefore, AB ‒ BA is a skew-symmetric matrix.
The correct answer is A.