Let A and B are two square matrices of order 3 such that det. `(A)=3` and det. `(B)=2`, then the value of det. `(("adj. "(B^(-1) A^(-1)))^(-1))` is eq

Question

Let A and B are two square matrices of order 3 such that det. `(A)=3` and det. `(B)=2`, then the value of det. `(("adj. "(B^(-1) A^(-1)))^(-1))` is eq

Let A and B are two square matrices of order 3 such that det. `(A)=3` and det. `(B)=2`, then the value of det. `(("adj. "(B^(-1) A^(-1)))^(-1))` is equal to _______ .

Monjur Alahi

7 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 36
`("adj. "(B^(-1) A^(-1)))^(-1)=("adj. "(AB)^(-1))^(-1)`
`=(("adj. "(AB))^(-1))^(-1)" "["as adj. "A^(-1)=("adj. A")^(-1)]`
= adj. (AB)
`:. |("adj. (AB)")|=|AB|^(2)=|A|^(2)|B|^(2)=9xx4=36`

7 views Answered 2023-02-05 15:29