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set of all possible diagonal matrix of order n

ans given monoid

my doubt-why it cannot have inverse??
in Set Theory & Algebra by (437 points)
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Can you guarantee that "Every Diagonal matrix" will be non-singular?
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a diagonal matrix is the one in which the prinicipal diagonal elements are non zero....so yes it is non singular
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Correct . Is there any other criteria given regarding matrix in the question?
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no
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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.
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yes i was also thinking the same now...

may be u are correct ...

anyways thanks

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