Let A be a square matrix of order 3 such that det. `(A)=1/3`, then the value of det. `("adj. "A^(-1))` is

Let A be a square matrix of order 3 such that det. `(A)=1/3`, then the value of det. `("adj. "A^(-1))` is
A. `1//9`
B. `1//3`
C. `3`
D. `9`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

Correct Answer - D
We know that det. (adj. A)`=("det. A")^(n-1)`, where `n` is order of matrix A.
For `n=3`, det `("adj. "A^(-1))=("det. "A^(-1))^(2)=1/(("det. A")^(2))=9`

4 views Answered 2023-02-05 15:29

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