Let A be a 2 - 2 matrix Statement - I - adj adj A - A Statement - II - -adj A - A -A- Both I and II are trueB- Both I and II are falseC- I is true but II is falseD- I is false but II is true

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

Byju's Answer

Standard XII

Mathematics

Inequality

Let A be a 2 ...

Question

Let A be a $2 \times 2$ matrix
Statement - I : adj (adj A) = A
Statement - II : |adj A| = |A|

Both (I) and (II) are true

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

Both (I) and (II) are false

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

(I) is true but (II) is false

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

(I) is false but (II) is true

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

Open in App

Solution

The correct option is A Both (I) and (II) are true
$| a d j A | = | A |^{n - 1} = | A |^{2 - 1} = | A | a d j (a d j A) = | A |^{n - 2} A + | A |^{\circ} A = A$

Suggest Corrections

Similar questions

Q. Let

A^{- 1}

be a

3 \times 3

matrix such that

A^{2} - 5 A + 7 I = 0.

Statement-I :-

A^{- 1} = \frac{1}{7} (5 I - A) .

Statement-II :-The polynomial

A^{3} - 2 A^{2} - 3 A + I

can be reduced to

5 (A - 4 I)

.Then

Observe the following statements

$(i) I n Δ A B C, b c o s^{2} \frac{C}{2} + c c o s^{2} \frac{B}{2} = s$

$(i i) I n Δ A B C, c o t \frac{A}{2} = \frac{b + c}{a} \Rightarrow B = 90^{0}$

Which of the following is correct?

Q. Statement I: Two atoms of X combine with three atoms of Y to form

X_{2} Y_{3}

.

Statement II: From the chemical formula of the compound

X_{2} Y_{3}

, we can conclude that the valency of X is 2.

Statement-I : A charged plane parallel plate capacitor has half interplanar region (I) filled with dielectric slab. The other half region II has air. Then, the magnitude of net electric field in region I is less than that in region II.

Statement-II : In a dielectric medium, induced (or polarized) charges tend to reduce the electric field.

Question 23

Statements (I) and (II) are as given below:
I: If two lines intersect, then the vertically opposite angles are equal.
II: If a transversal intersects two other lines, then the sum of two interior angles on the same side of the transversal is $180^{\circ}$ .

Then,
(a) both (I) and (II) are true
(b) (I) is true and (II) is false
(c) (I) is false and (II) is true
(d) both (I) and (II) are false

Join BYJU'S Learning Program

Let A be a 2×2 matrix Statement - I : adj (adj A) = A Statement - II : |adj A| = |A|

The correct option is A Both (I) and (II) are true|adjA|=|A|n−1=|A|2−1=|A|adj(adjA)=|A|n−2A+|A|∘A=A

Let A be a $2 \times 2$ matrix
Statement - I : adj (adj A) = A
Statement - II : |adj A| = |A|

The correct option is A Both (I) and (II) are true
$| a d j A | = | A |^{n - 1} = | A |^{2 - 1} = | A | a d j (a d j A) = | A |^{n - 2} A + | A |^{\circ} A = A$