# 2×2matrix having elements 0 and 1 is selected at random.probability that it's a non singular matrix?

##### 1 Answer

May 3, 2018

#### Explanation:

First of all, we must observe that there are 16 possible matrices: we have to fill

Let's think about the number of zero elements:

- if all elements are zero, then the determinant is surely zero
- if three elements are zero, then we have a zero row and a zero column. Both of these conditions are sufficient for the determinant to be zero
- if two elements are zero, for the same reason, they can't be aligned vertically or horizontally.
- If one element is zero, the matrix is invertible
- If all elements are ones, then the matrix has two identical rows/columns, and the determinant is again zero

So, by the point (4), you have to chose the spot to be zero, and you have four choices:

Plus, the two diagonal matrix in point (3):

So,