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

Byju's Answer

Standard XII

Mathematics

Involutory Matrix

If A is an id...

Question

If $A$ is an idempotent matrix of index $2,$ then which of the following statement(s) is/are true ?
$I .$ $I + A$ is idempotent.
$I I .$ $I - A$ is idempotent.

Only

I

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

Only

I I

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

both

I

and

I I

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

neither

I

nor

I I

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

Open in App

Solution

The correct option is B Only $I I$
$(I + A)^{2} = I^{2} + 2 I A + A^{2} = I + 2 A + A (∵ A^{2} = A) = I + 3 A$
$(I - A)^{2} = I^{2} - 2 I A + A^{2} = I - 2 A + A (∵ A^{2} = A) = I - A$
Only $I I$ is true.

Suggest Corrections

Similar questions

Q. Which of the following two groups of people have identical sources?
(i) A, D and G
(ii) E and H

Q. Let

f : [1, \infty) \to R

be a function defined by

f (x) = x x \int 1 \frac{e^{t}}{t} d t - e^{x}

f (x)

is an increasing function.
II.

lim x \to \infty f (x) = 0

Which of the following statements are correct?

Q. For an LPP,
Maximize

Z = a x + b y

where

a, b \in R

subject to the constraints :

a_{1} x + b_{1} y \leq 0

a_{2} x + b_{2} y \leq 0

x, y \geq 0

,
consider the following statements:

(I)

The solution depends on the optimizing function.

(I I)

The solution depends on the constraints.

Which of the following statement(s) is/are correct?

(a)

Only

(I)

(b)

Only

(I I)

(c)

Both

(I)

and

(I I)

(d)

Neither

(I)

nor

(I I)

Q. Lewis acids among the following are
(i)

C C l_{4}

(ii)

S i C l_{4}

(iii)

G e F_{4}

If $x = 0. ¯ 18$ , which of the following statements are true?

(i) $100 x = 18. ¯ 18$
(ii) $100 x - x = 17. ¯ 18$
(iii) $99 x = 18$

Join BYJU'S Learning Program

If A is an idempotent matrix of index 2, then which of the following statement(s) is/are true ? I. I+A is idempotent. II. I−A is idempotent.

The correct option is B Only II (I+A)2=I2+2IA+A2 =I+2A+A (∵A2=A) =I+3A (I−A)2=I2−2IA+A2 =I−2A+A (∵A2=A) =I−A Only II is true.

If $A$ is an idempotent matrix of index $2,$ then which of the following statement(s) is/are true ?
$I .$ $I + A$ is idempotent.
$I I .$ $I - A$ is idempotent.

The correct option is B Only $I I$
$(I + A)^{2} = I^{2} + 2 I A + A^{2} = I + 2 A + A (∵ A^{2} = A) = I + 3 A$
$(I - A)^{2} = I^{2} - 2 I A + A^{2} = I - 2 A + A (∵ A^{2} = A) = I - A$
Only $I I$ is true.