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

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.

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.

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.

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.

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.