If a is non singular matrix of order 3 such that |a
|=2 then find the value of |-3a^-1|
Answers
Answer:
\textbf{Concept:}Concept:
\text{If A and B are square matrices of same order, then}If A and B are square matrices of same order, then
\boxed{\bf\,det(AB)=det(A)\,det(B)}
det(AB)=det(A)det(B)
\text{If A is a square matrix of order n, then}If A is a square matrix of order n, then
\boxed{\bf\,det(kA)=k^n\;det(A)}
det(kA)=k
n
det(A)
\textbf{Given:}Given:
A^2 = 3AA
2
=3A
\textbf{To find:}\;det(A)To find:det(A)
\text{Now,}Now,
A^2 = 3AA
2
=3A
det(A^2) = det(3A)det(A
2
)=det(3A)
det(AA) = det(3A)det(AA)=det(3A)
det(A)\;det(A) = 3^3det(A)det(A)det(A)=3
3
det(A)
\implies\boxed{\bf\,det(A) = 27}⟹
det(A)=27
\therefore\textbf{The value of det(A) is 27}∴The value of det(A) is 27
\implies\bf\;\textbf{option (D) is correct}⟹option (D) is correct
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