CUET Preparation Today
If A and B are any symmetric matrices each of order $3×3$ then $AB - BA$ is : |
a symmetric matrix a skew-symmetric matrix a zero matrix an identity matrix |
a skew-symmetric matrix |
The correct answer is Option (2) → a skew-symmetric matrix $(AB-BA)^T=(AB)^T-(BA)^T$ $B^TA^T-A^TB^T$ $=BA-AB$ [A and B = Symmetric] $=-(AB-BA)$ ∴ skew-symmetric |
