Ex 3.3, 11 (MCQ) - Chapter 3 Class 12 Matrices
Last updated at April 16, 2024 by Teachoo
Proof using property of transpose
Chapter 3 Class 12 Matrices
Concept wise
- Formation and order of matrix
- Types of matrices
- Equal matrices
- Addition/ subtraction of matrices
- Statement questions - Addition/Subtraction of matrices
- Multiplication of matrices
- Statement questions - Multiplication of matrices
- Solving Equation
- Finding unknown - Element
- Finding unknown - Matrice
- Transpose of a matrix
- Symmetric and skew symmetric matrices
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Proof using property of transpose
- Inverse of matrix using elementary transformation
- Proof using mathematical induction
Transcript
Ex 3.3, 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 Since A and B are symmetric matrices, ∴ A’ = A and B’ = B Now, (AB – BA)’ = (AB)’ – (BA)’ = B’A’ – A’B’ = BA − AB = − (AB – BA) Since(AB – BA)’ = − (AB – BA) Thus, (AB − BA) is a skew-symmetric matrix. ∴ Correct answer is A. ∴ Correct answer is A.
