3 and 4 .Determinants and Matrices
normal

જો $ABC = I$ હોય તો  $tr(ABC + BCA + CAB)$ મેળવો .        (કે જ્યાં  $A, B, C$ ની કક્ષા $3$ છે અને $tr(A)$ એ $A$ ના વિકર્ણના ઘટકોનો સરવાળો છે .)

A

$3$

B

$9$

C

$12$

D

$15$

Solution

$\mathrm{ABC}=\mathrm{I}$

$\mathrm{BC}=\mathrm{A}^{-1}$

$\mathrm{BCA}=\mathrm{I}$

$\mathrm{BC}=\mathrm{A}^{-1}$

$\mathrm{C}=\mathrm{B}^{-1} \mathrm{A}^{-1}$

$\mathrm{CA}=\mathrm{B}^{-1} \Rightarrow \mathrm{CAB}=\mathrm{I}$

$\operatorname{tr}(3 \mathrm{I})=9$

Standard 12
Mathematics

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