If A is 2- 2 matrix such that A2 - 0- then tr A is

The correct option is A 0If A = 0,tr(A)=0 . Suppose A≠ 0 and A =[ a amp;b; c amp;d ] , then |A|=0 and A^2 (a+d)A+ad bc=0 ...

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Standard XII

Mathematics

Inverse of a Function

If A is 2...

Question

If $A$ is $2 \times 2$ matrix such that $A^{2} = 0$ , then $t r (A)$ is

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-1

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none of these

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Solution

The correct option is A 0
If $A = 0, t r (A) = 0$ .
Suppose $A \neq 0$ and $A = [\begin{matrix} a & b c & d \end{matrix}]$ , then $| A | = 0$ and
$A^{2} - (a + d) A + a d - b c = 0$
$\Rightarrow a + d = 0$
$∴ t r (A) = 0$
Hence, option B.

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Similar questions

Q. Assertion :Let

A

be a

2 \times 2

matrix with real entries. Let

I

be the

2 \times 2

identity matrix. Denote by

t r (A)

, the sum of diagonal entries of

A

. Assume that

A^{2} = I

A \neq I

and

A \neq - I

, then

d e t (A) = - 1

Reason: If

A \neq I

and

A \neq - I

, then

t r (A) \neq 0

Q. Let A be a

2 \times 2

matrix with non-zero entries and let

A^{2} = I

, where I is

2 \times 2

identity matrix. Define Tr(A)

=

sum of diagonal elements of A and

| A | =

determinant of matrix A.
Statement-1 Tr(A)

= 0

Statement-2:

| A | = 1

Q. If

A

is a matrix such that

A^{2} + A + 2 I = 0

, then which of the following is/are true?

Q. If A is matrix of size

n \times n

such that

A^{2} + A + 2 = O,

Let

A

be a matrix of order

2 \times 2

such that

A^{2} = 0

then

A^{2} - (a + d) A + (a d - b c) I

is equal to

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If A is 2×2 matrix such that A2=0, then tr(A) is

The correct option is A 0If A=0,tr(A)=0. Suppose A≠0 and A=[abcd], then |A|=0 and A2−(a+d)A+ad−bc=0⇒a+d=0∴tr(A)=0Hence, option B.

If $A$ is $2 \times 2$ matrix such that $A^{2} = 0$ , then $t r (A)$ is

The correct option is A 0
If $A = 0, t r (A) = 0$ .
Suppose $A \neq 0$ and $A = [\begin{matrix} a & b c & d \end{matrix}]$ , then $| A | = 0$ and
$A^{2} - (a + d) A + a d - b c = 0$
$\Rightarrow a + d = 0$
$∴ t r (A) = 0$
Hence, option B.