JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q64

MathematicsSingle correct+4 / -1Question 64 of 90

Let A and B be any two 3×3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB − BA is :

skewsymmetric

symmetric

neither symmetric nor skewsymmetric

I or −I, where I is an identity matrix.

Answer and worked solution

Official answer: B

With $A^T=A$ and $B^T=-B$ :
$(AB-BA)^T=B^TA^T-A^TB^T=-BA+AB=AB-BA.$
So $AB-BA$ is symmetric.

JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 64