Matrices Test

Result

Matrices Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

If a matrix A is symmetric as well as skew symmetric, then A is a

A
unit matrix

B
diagonal matrix

C
null matrix

D
none of these

Solution

Only a null matrix can be symmetric as well as skew symmetric.

In Symmetric Matrix A^T= A,

Skew Symmetric Matrix A^T= -A,

Given that the matrix is satisfying both the properties.Therefore, Equating the RHS we get A = -A i.e 2A = 0 .

Therefore A=0,which is a null matrix.
Question 2
1 / -0

A square matrix A is called idempotent if

A
2A=I

B
A² = O

C
A² = I

D
A² = A

Solution

If the product of any square matrix with itself is the matrix itself, then the matrix is called Idempotent.
Question 3
1 / -0

If A and B are invertible matrices of the same order, then (AB)^-1 is equal to

A
A^-1B

B
AB^-1

C
A^-1B^-1

D
B^-1A^-1

Solution

By the property of inverse (AB)^-1 is equal to B^-1A^-1.
Question 4
1 / -0

Let A be any m×nm×n matrix, then A² can be found only when

A
m < n

B
m > n

C
m = n

D
none of these

Solution

The product of any matrix with itself can be found only when it is a square matrix .i.e. m=n.
Question 5
1 / -0

If A and B are any two matrices, then

A
AB = O

B
2A²

C
A²= O

D
AB may or may not be defined.

Solution

Let matrix A is of order m x n, and matrix B is of order p x q. Then, the product AB is defined only when n = p. That’s why, If A and B are any two matrices, then AB may or may not be defined.

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Matrices Test - 4

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Matrices Test - 4

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Question 1

unit matrix

diagonal matrix

null matrix

none of these

Solution

Question 2

2A=I

A2 = O

A2 = I

A2 = A

Solution

Question 3

A-1B

AB-1

A-1B-1

B-1A-1

Solution

Question 4

m < n

m > n

m = n

none of these

Solution

Question 5

AB = O

2A2

A2 = O

AB may or may not be defined.

Solution

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A² = O

A² = I

A² = A

A^-1B

AB^-1

A^-1B^-1

B^-1A^-1

2A²

A²= O