If A is a 3 - 3 matrix and det A-5- then det adj A is equal toA- 5B- 25C- 125 1D- 5

The correct option is B 25We know that, if A is a n^th order square matrix, then nbsp; (adj A)=( A)^n 1 Here, n=3 and A=5 ∴(adj A)=( A)^3 1=( A)^2 =5^2 =25 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties of Determinants

If A is a 3 ×...

Question

If $A$ is a $3 \times 3$ matrix and $det A = 5,$ then $det (a d j A)$ is equal to

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

25

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

125

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $25$
We know that, if $A$ is a $n^{t h}$ order square matrix, then
$det (a d j A) = (det A)^{n - 1}$
Here, $n = 3$ and $det A = 5$
$∴ det (a d j A) = (det A)^{3 - 1} = (det A)^{2}$
$= 5^{2}$
$= 25$

Suggest Corrections

Similar questions

Q. If

A

is a

3 \times 3

matrix and

det A = 5,

then

det (a d j A)

is equal to

Q. Observe the following lists :
List - I List - II
A) If A is a singular 1)

{(d e t A)}^{n - 1}

matrix then adj A is
B) If A is a square 2) an idempotent Matrix
matrix then detA=
C) If

A^{2}

=A then A is 3) Singular
D) If A is square matrix 4)

d e t A^{T}

of type n then det (adj A) = 5) a nil potent matrix
The correct match for list - I from list - II is

Q. For a 3 X 3 matrix A, if det A = 4, then det (Adj. A) equals

S_{1} :

For a

3 * 3

square matrix A if adj(adj A) = (det A) A then det (adj A) =

{(d e t A)}^{2}

S_{2} :

For a

3 * 3

square matrix a if det (2A) = 8(det A) then det

a d j (2 A) = 8 | a d j A |

Q. Assertion :If

A

is skew symmetric matrix of order

3 \times 3

, then

d e t (A) = 0

| A | = 0

Reason: If

A

is a square matrix, then

d e t (A) = d e t (A)^{'} = d e t ({- A}^{^{'}})

Join BYJU'S Learning Program

If A is a 3×3 matrix and detA=5, then det(adj A) is equal to

The correct option is B 25We know that, if A is a nth order square matrix, then det(adj A)=(detA)n−1 Here, n=3 and detA=5 ∴det(adj A)=(detA)3−1=(detA)2 =52 =25

If $A$ is a $3 \times 3$ matrix and $det A = 5,$ then $det (a d j A)$ is equal to

The correct option is B $25$
We know that, if $A$ is a $n^{t h}$ order square matrix, then
$det (a d j A) = (det A)^{n - 1}$
Here, $n = 3$ and $det A = 5$
$∴ det (a d j A) = (det A)^{3 - 1} = (det A)^{2}$
$= 5^{2}$
$= 25$