A square matrix [aij] such that aij=0 for i≠j and aij=k where k is a constant for i=j is called
A
Diagonal as well as scalar matrix
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B
Scalar matrix
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C
Unit matrix
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D
None of the above
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Solution
The correct option is C Diagonal as well as scalar matrix By given, we can construct a matrix as below
=⎡⎢
⎢
⎢
⎢
⎢
⎢⎣k0...000k....0............0..0k000...0k⎤⎥
⎥
⎥
⎥
⎥
⎥⎦ Clearly the matrix is a diagonal matrix as all non diagonal elements are zero. Also, the matrix is also a scalar matrix because all diagonal elements are same and non diagonal elements are zero. So, option A is correct.