In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer- Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix. Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.
a)
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
b)
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
c)
Assertion is true but Reason is false.
d)
Assertion is false but Reason is true.
Correct answer is option 'A'. Can you explain this answer?
A scalar matrix is a square matrix in which it's diagonal elements are of equal magnitude/same value and all other elements are zero .So a scalar matrix is a multiple of identity matrix(i.e,kI). So it follows commutative law (AB=BA or A+B=B+A)(In the given question commutes means obeying commutative law)
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A scalar matrix is a square matrix in which it's diagonal elements are of equal magnitude/same value and all other elements are zero .So a scalar matrix is a multiple of identity matrix(i.e,kI). So it follows commutative law (AB=BA or A+B=B+A)(In the given question commutes means obeying commutative law)
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