jee-main 2022 Q67

jee-main · India · session2_28jul_shift2 Matrices Matrix Algebra and Product Properties

Let $A$ and $B$ be any two $3 \times 3$ symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?
(1) $A ^ { 4 } - B ^ { 4 }$ is a symmetric matrix
(2) $A B - B A$ is a symmetric matrix
(3) $B ^ { 5 } - A ^ { 5 }$ is a skew-symmetric matrix
(4) $A B + B A$ is a skew-symmetric matrix

Let $A$ and $B$ be any two $3 \times 3$ symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?\\
(1) $A ^ { 4 } - B ^ { 4 }$ is a symmetric matrix\\
(2) $A B - B A$ is a symmetric matrix\\
(3) $B ^ { 5 } - A ^ { 5 }$ is a skew-symmetric matrix\\
(4) $A B + B A$ is a skew-symmetric matrix

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