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?

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Answers

Putta Sarmishta
May 30, 2022
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)

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)
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)