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Made Easy Test Series 2019: Set theory & Algebra - Groups
0
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set of all possible diagonal matrix of order n
ans given monoid
my doubt-why it cannot have inverse??
discrete-mathematics
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asked
Jan 24, 2019
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priyanka manwani
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Mar 3, 2019
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ajaysoni1924
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Can you guarantee that "Every Diagonal matrix" will be non-singular?
0
a diagonal matrix is the one in which the prinicipal diagonal elements are non zero....so yes it is non singular
0
Correct . Is there any other criteria given regarding matrix in the question?
0
no
0
Inverse of a diagonal matrix is obtained by taking reciprocal of the diagonal elements .
i.e if a diagonal element is a1 , in inverse it will be 1/a1.
But what if a1=0?
A diagonal matrix cannot have all elements as 0 , but it can have 0 elements right?
In that case , 1/0 is undefined.
0
yes i was also thinking the same now...
may be u are correct ...
anyways thanks
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Zero matrix is also diagonal matrix and we know we can’t have inverse for the matrix for which determinant == 0
so for Zero matrix we can’t have inverse => G is not a group
But other Property like Closure , Associativity (Matrix multiplication is Associative) and identity element ( identity matrix is identity element for Matrix Multiplication ) is there so it is monoid
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Sep 17
Dhruvil
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