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Adjoint of a Matrix

adj adj A = |...

Question

$a d j (a d j A) = | A |^{n - 2} A$

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Solution

$A a d j A = | A | I_{n}$
Replace 'A' with $(a d j A)$
$(a d j A) (a d j (a d j A)) = | a d j A | I_{n}$
$A . a d j A a d j (a d j A) = A | A |^{n - 1} I_{n}$
$| A | I_{n} a d j (a d j A) = A | A |^{n - 1} A$
$a d j (a d j A) = | A |^{n - 2} . A$

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Similar questions

Q. Statement - 1:

A = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 3 & 4 2 & - 3 & 4 0 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦

a d j (a d j A) = A

Statement - 2 : If A is a square matrix of order n, then

a d j (a d j A) = {| A |}^{n - 2} A

Q. Statement - 1 : If

A

is an orthogonal matrix of order

n

| a d j (a d j A) | = \pm 1

Statement - 2 :

| a d j (a d j A) | = {| A |}^{n^{2} - 1}

Q. Statement-1 : If

A = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 3 & 4 2 & - 3 & 4 0 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦

a d j (a d j A) = A

| a d j (a d j A) | = | A |^{(n - 1)^{2}}

, where A is a n-rowed non-singular square matrix

If A is a n x n matrix, then adj(adj A) =

A

is a square matrix of order

m \times n

a d j (a d j A)

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