Matrices Test

Result

Matrices Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

If A and B are two matrices such that A + B and AB are both defined, then

A
number of columns of A = number of rows of B.

B
A and B are square matrices of same order

C
A, B are square matrices not necessarily of same order

D
A and B can be any matrices

Solution

If A and B are square matrices of same order, both operations A + B and AB are well defined.
Question 2
1 / -0

From the matrix equation AB = AC we can conclude B = C, provided

A
A is symmetric matrix

B
A is non-singular matrix

C
A is square matrix

D
A is singular matrix

Solution

Here, only non- singular matrices obey cancellation laws.
Question 3
1 / -0

If A and B are two non-zero square matrices such that AB = 0, then

A
either of them is singular

B
neither matrix is singular

C
both A and B are singular

D
none of these

Solution

The product of two non-zero matrices can be a zero matrix if one of the two given matrices should be singular.
Question 4
1 / -0

If A and B are two matrices such that AB = BA and BA = A, then A² + B²=

A
2 BA

B
AB

C
2 AB

D
A + B

Solution

AB = B ⇒ (AB)A = BA

⇒ A(BA) = BA ⇒ A(A) = A,

⇒ A² = A

AB = B ⇒ B(AB) = BB

⇒ (BA)B = B²

^⇒AB = B²

⇒ B = B²

∴ A² + B² = A + B