Question:medium
Let \(A=[a_{ij}]\), \(\det(A)\neq 0\), and \(B=[b_{ij}]\) be two \(3\times 3\) matrices.
If
\[
b_{ij}=3^{\,i-j}\,a_{ij}\quad \text{for all } i,j=1,2,3,
\]
then:
Let \(A=[a_{ij}]\), \(\det(A)\neq 0\), and \(B=[b_{ij}]\) be two \(3\times 3\) matrices.
If
\[
b_{ij}=3^{\,i-j}\,a_{ij}\quad \text{for all } i,j=1,2,3,
\]
then:
Show Hint
When each element is multiplied by \(k^{i-j}\),
separate the effect into \textbf{row scaling} and \textbf{column scaling}.
If total row and column powers cancel, the determinant remains unchanged.
Updated On: Mar 3, 2026
- \(3\det(A)=\det(B)\)
- \(27\det(A)=\det(B)\)
- \(\det(A)=\det(B)\)
- \(\det(A)=27\det(B)\)
Show Solution
The Correct Option is C
Solution and Explanation
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