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Derivative of Standard Functions

If A is a n x...

Question

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

A

|A|^n-1 A

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B

|A|^n-2 A

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C

|A|ⁿ A

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D

None of these

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Solution

The correct option is B
|A|^n-2 A

We know by the fundamental concept that adj(adj 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

A

is a square matrix of order

m \times n

a d j (a d j A)

A

is a non-singular square matrix of order

n,

a d j (a d j (A))

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