jee-main 2025 Q68

jee-main · India · session2_03apr_shift1 3x3 Matrices Determinant of Parametric or Structured Matrix
Q68. Let $A$ and $B$ be two square matrices of order 3 such that $| A | = 3$ and $| B | = 2$. Then $\left| \mathrm { A } ^ { \mathrm { T } } \mathrm { A } ( \operatorname { adj } ( 2 \mathrm {~A} ) ) ^ { - 1 } ( \operatorname { adj } ( 4 \mathrm {~B} ) ) ( \operatorname { adj } ( \mathrm { AB } ) ) ^ { - 1 } \mathrm { AA } ^ { \mathrm { T } } \right|$ is equal to :
(1) 108
(2) 32
(3) 81
(4) 64
Q68. Let $A$ and $B$ be two square matrices of order 3 such that $| A | = 3$ and $| B | = 2$. Then $\left| \mathrm { A } ^ { \mathrm { T } } \mathrm { A } ( \operatorname { adj } ( 2 \mathrm {~A} ) ) ^ { - 1 } ( \operatorname { adj } ( 4 \mathrm {~B} ) ) ( \operatorname { adj } ( \mathrm { AB } ) ) ^ { - 1 } \mathrm { AA } ^ { \mathrm { T } } \right|$ is equal to :\\
(1) 108\\
(2) 32\\
(3) 81\\
(4) 64