# what does this question about a matrix mean?

here is a question says :

what does that mean ?

I did my best to solve this question myself but i didn't find a way to solve it

is this question possible or there is something else that i don't understand it

the matrix is square ..

how it changes to singular?

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## 1 Answer

A singular matrix is a matrix which does not have an inverse. A matrix has an inverse if and only if its determinant is nonzero. Take the determinant and find the value(s) of $\alpha$ which makes the determinant zero. Then just take the $\alpha$ such that it means the condition of the problem - that is, $0 \leq \alpha <2\pi$.

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THANKS ! .......... ..... – Maher May 19 '14 at 21:18
but ! we know that a matrix of order " size " $n*n$ is called a square matrix .. and the above matrix is $2*2$ matrix .. so even if it has not an inverse it is still square ?? confusion ?? – Maher May 19 '14 at 21:32
We only consider the determinant for square matrices and the only consider matrices to even possibly having an inverse if the matrix is square. But keep in mind just because a matrix is square doesn't mean that it will have an inverse. So to sum up, for the question asking about a determinant of a matrix or its inverse, the question only makes sense if the matrix is square. But just being square isn't enough. There is more to check - that is, that the determinant of the matrix is not zero. You need both square AND nonzero determinant. – mathematics2x2life May 19 '14 at 21:36