If ∣AdjA∣=81, find ∣A∣ if A is a matrix of order 3×3. Find also ∣AT∣ & A−1

We know that∣adjA∣=∣A∣n−1 n=3∣n∣2=81⇒∣A∣=9∣A−1∣=∣A∣1=91∣A∣=−∣A∣=−9

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If |Adj, A | = 81, find |A| if A is a matrix of order 3 3. Fin

Question

If $∣ A d j A ∣ = 81$ , find $∣ A ∣$ if $A$ is a matrix of order $3 \times 3$ . Find also $∣ A^{T} ∣$ & $A^{- 1}$

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Harper Discussed

∣ A d j A ∣ = 81

, find

∣ A ∣

A

is a matrix of order

3 \times 3

. Find also

∣ A^{T} ∣

A^{- 1}

11 mins ago

Discuss this question LIVE

11 mins ago

We know that

∣ a d j A ∣ = ∣ A ∣^{n - 1}

n = 3

∣ n ∣^{2} = 81

\Rightarrow ∣ A ∣ = 9

∣ A^{- 1} ∣ = \frac{1}{∣ A ∣} = \frac{1}{9}

∣ A ∣ = - ∣ A ∣ = - 9

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Question Text	If $∣ A d j A ∣ = 81$ , find $∣ A ∣$ if $A$ is a matrix of order $3 \times 3$ . Find also $∣ A^{T} ∣$ & $A^{- 1}$
Answer Type	Text solution:1
Upvotes	150