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Test: Matrices- Assertion & Reason Type Questions - JEE MCQ


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5 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Matrices- Assertion & Reason Type Questions

Test: Matrices- Assertion & Reason Type Questions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Matrices- Assertion & Reason Type Questions questions and answers have been prepared according to the JEE exam syllabus.The Test: Matrices- Assertion & Reason Type Questions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Matrices- Assertion & Reason Type Questions below.
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Test: Matrices- Assertion & Reason Type Questions - Question 1

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): If A is a square matrix such that A2 = A, then (I + A)2 – 3A = I
Reason (R): AI = IA = A

Detailed Solution for Test: Matrices- Assertion & Reason Type Questions - Question 1

AI = IA = A is true.
Hence R is true.
Given A2 = A,
∴ (I + A)2 - 3A = I2 + 2IA + A2 - 3A
= I + 2A + A - 3A
= I
Hence A is true.
R is the correct explanation for A.

Test: Matrices- Assertion & Reason Type Questions - Question 2

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
A and B are two matrices such that both AB and BA are defined.
Assertion (A): (A + B)(A – B) = A2 – B2
Reason (R): (A + B)(A – B) = A2 – AB + BA – B2

Detailed Solution for Test: Matrices- Assertion & Reason Type Questions - Question 2

For two matrices A and B, even if both AB and BA are defined, generally AB ≠ BA.
(A + B)(A – B) = A2 – AB + BA – B2.
Since AB ≠ BA, (A + B)(A – B) ≠ A2 – B2.
Hence R is true and A is false.

Test: Matrices- Assertion & Reason Type Questions - Question 3

 Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): (A + B)2 ≠ A2 + 2AB + B2.
Reason (R): Generally AB ≠ BA

Detailed Solution for Test: Matrices- Assertion & Reason Type Questions - Question 3

For two matrices A and B, generally AB ≠ BA.
i.e., matrix multiplication is not commutative.
∴ R is true
(A + B)2 = (A + B)(A + B)
= A2 + AB + BA + B2 ≠ A2 + 2AB + B2
∴ A is true
R is the correct explanation for A.

Test: Matrices- Assertion & Reason Type Questions - Question 4

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Let A and B be two symmetric matrices of order 3.
Assertion (A): A(BA) and (AB)A are symmetric matrices.
Reason (R): AB is symmetric matrix if matrix multiplication of A with B is commutative.

Detailed Solution for Test: Matrices- Assertion & Reason Type Questions - Question 4

Generally (AB)’ = B’ A’
If AB = BA, then (AB)’ = (BA)’ = A’ B’ = AB
Since (AB)’ = AB, AB is a symmetric matrix. Hence R is true.
A(BA) = (AB)A = ABA
(ABA)’ = A’ B’ A’ = ABA.
A(BA) and (AB)A are symmetric matrices. Hence A is true.
But R is not the correct explanation for A.

Test: Matrices- Assertion & Reason Type Questions - Question 5

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): is a scalar matrix.
Reason (R): If all the elements of the principal diagonal are equal, it is called a scalar matrix.

Detailed Solution for Test: Matrices- Assertion & Reason Type Questions - Question 5

In a scalar matrix the diagonal elements are equal and the non-diagonal elements are zero. Hence R is false.
A is true since the diagonal elements are equal and the non-diagonal elements are zero.

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