if 'A' is non - singular square matrix of order 3, then $∣ ∣ a d j (A^{3}) ∣ ∣$ equals

{| A |}^{8}

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{| A |}^{6}

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{| A |}^{9}

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{| A |}^{12}

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Solution

The correct option is C ${| A |}^{6}$
$| a d j (B) | = {| B |}^{n - 1}$
if $B = A^{3}$
then $∣ ∣ a d j {(A)}^{3} ∣ ∣ = {∣ ∣ A^{3} ∣ ∣}^{2} = {| A |}^{6}$

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Similar questions

Q. If

A

' is non-singular square matrix of order 3 then

| a d j (A^{3}) |

equals

Let A be the non-singular square matrix of order $3 \times 3$ then |adj A| is equal to

a) $| A |$
b) $| A |^{2}$
c) $| A |^{3}$
d) $3 | A |$

If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
(a) null matrix
(b) singular matrix
(c) unit-matrix
(d) non-singular matrix

Q. If

A

is a non-singular square matrix of order

n,

then

a d j (a d j (A))

is equal to

Q. If

A

is a non singular square matrix of order

3 \times 3

, find

| a d j A |

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if 'A' is non - singular square matrix of order 3, then ∣∣adj(A3)∣∣ equals

The correct option is C |A|6|adj(B)|=|B|n−1if B=A3then ∣∣adj(A)3∣∣=∣∣A3∣∣2=|A|6

if 'A' is non - singular square matrix of order 3, then $∣ ∣ a d j (A^{3}) ∣ ∣$ equals

The correct option is C ${| A |}^{6}$
$| a d j (B) | = {| B |}^{n - 1}$
if $B = A^{3}$
then $∣ ∣ a d j {(A)}^{3} ∣ ∣ = {∣ ∣ A^{3} ∣ ∣}^{2} = {| A |}^{6}$