Q. 15.0( 1 Vote )

Which one of the following statements is not true?
A. A scalar matrix is a square matrix

B. A diagonal matrix is a square matrix

C. A scalar matrix is a diagonal matrix

D. A diagonal matrix is a scalar matrix.

Answer :

In the above question we see the following terms,


Scalar Matrix, Square Matrix, Diagonal Matrix


To answer this question, we have to know the definition of the above terms.


Square Matrix:


If the rows and columns of the matrices are equal then it will constitute square like structure. So, it is called as square matrix.


E.g.


Diagonal Matrix:


In a square matrix all the elements are zero except the diagonal elements of the matrix. Then that matrix is said to be diagonal matrix.


E.g.


Scalar Matrix:


In a diagonal matrix, if all the diagonal elements are same then that matrix is said to be a scalar matrix.


E.g.


Option(A):


A scalar matrix should be a square matrix so, it is true


Option(B):


Diagonal matrix forms only with the square matrix so, it is true


Option(C):


A scalar matrix consists of zero except the diagonal elements so it is true.


Option(D):


A scalar matrix should comprise of same diagonal elements but in diagonal matrix it may (or) may not contains same diagonal elements. So it is False.


Option(D) is not True in the given.

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