Match the properties of adjoint of a matrix -Adj nbsp-A-TAdj nbsp-B nbsp- nbsp-Adj nbsp-A nbsp- nbsp- nbsp-AN-1 nbsp-N is order of A

The correct option is →adj A=AA 1adj A=AA 1= nbsp;AN1A=ANA 1=AN 1→Adj nbsp;AB=ABAB 1=ABB 1A 1=BB 1 nbsp;AA 1=Adj nbsp;B.Adj nbsp;A→Adj nbsp;AT=AT 1 ...

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Byju's Answer

Standard XII

Mathematics

Adjoint of a Matrix

Match the pro...

Question

Match the properties of adjoint of a matrix :-

{(A d j A)}^{T}

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A d j B . A d j A

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{(A)}^{^{N - 1}}

,N is order of

(A)

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Solution

$\to adj A = (A | A^{- 1} (adj A | = ((A | A^{- 1} ∣ ∣ = {(A |}^{N} \frac{1}{(A |} = {(A |}^{N} {(A |}^{- 1} = {(A |}^{N - 1} \to Adj AB = (AB | {(AB)}^{- 1} = (A | (B | B^{- 1} A^{- 1} = (B | B^{- 1} (A | A^{- 1} = Adj B . Adj A \to Adj (A^{T}) = {(A^{T})}^{- 1} (A^{T} ∣ ∣ = {(A^{- 1})}^{T} {(A |}^{T} (∵ {(A^{- 1})}^{T} = A^{T}, (A^{T} ∣ ∣ = {(A |}^{T}) {((A | A^{- 1})}^{T} = {(Adj A)}^{T}$

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Similar questions

Q. If A is an invertible matrix of order 3 and

|A| = 5, then adj (a d j A)

= __________________.

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and adj(A) denotes the inverse, transpose and adjoint of matrix A respectively) contains:

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Q. Let

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such that

∣ ∣ A + | A | adj (A) ∣ ∣ = 0,

then the value of

∣ ∣ A - | A | adj (A) ∣ ∣

Q. Assertion :

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| a d j A | = | A |^{n}

Q. If

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be a non-singular matrix of order

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such that

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Match the properties of adjoint of a matrix :-

→adjA=(A|A−1(adjA|=((A|A−1∣∣= (A|N1(A|=(A|N(A|−1=(A|N−1→Adj AB=(AB|(AB)−1=(A|(B|B−1A−1=(B|B−1 (A|A−1=Adj B.Adj A→Adj (AT)=(AT)−1(AT∣∣=(A−1)T(A|T (∵(A−1)T=AT, (AT∣∣=(A|T)((A|A−1)T=(Adj A)T