JEE Main 2022 · 28 Jul · Shift 2 · Mathematics Q63

MathematicsSingle correct+4 / -1Question 63 of 90

Let A and B be any two $3\times3$ symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?

A^4-B^4

is a smmetric matrix

AB-BA

is a symmetric matrix

B^5-A^5

is a skew-symmetric matrix

AB+BA

is a skew-symmetric matrix

Answer and worked solution

Official answer: C

Transposes. $A^5$ is symmetric and $B^5$ skew-symmetric, so $B^5-A^5$ is neither. (A), (B) and (D) all hold.

(C)

Topics:Special matrices

JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 63