Determinants Test

Result

Determinants Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

If A and B are invertible matrices of order 3, then det(adj A) =

A
1

B
(det A)²

C
|A|²

D
None of these

Solution

Let A be a non singular square matrix of order n then, det(adjA)=|A|^n-1

Here order is 3 so det(adj A)=|A|^3-1=|A|²
Question 2
1 / -0

If A is a square matrix of order 2, then det (adj A) =

A
I

B
|A|

C
2A²

D
A² = O

Solution

Let A be a square matrix of order 2 then |adj A| = |A|, because |adj A| =|A|^n-1 where n is the order of square matrix.
Question 3
1 / -0

If A is a non singular matrix of order 3 , then |adj(A³)|=

A
|A|⁶

B
None of these

C
|A|⁸

D
|A|⁹

Solution

If A is a non singular matrix of order 3, then |adj(A³)| = (|A³|)² = (|AAA|)² = (|A| |A| |A|)² = (|A|³)² = |A|⁶ .
Question 4
1 / -0

If I₃ is the identity matrix of order 3 , then I₃^-1 is

A
I₃

B
3I₃

C
0

D
None of these

Solution

Because, the inverse of an identity matrix is an identity matrix itself.

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Re-Attempt Weekly Quiz Competition

Determinants Test - 7

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Determinants Test - 7

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Question 1

1

(det A)2

|A|2

None of these

Solution

Question 2

I

|A|

2A2

A2 = O

Solution

Question 3

|A|6

None of these

|A|8

|A|9

Solution

Question 4

I3

3I3

0

None of these

Solution

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(det A)²

|A|²

2A²

A² = O

|A|⁶

|A|⁸

|A|⁹

I₃

3I₃