Is a matrix populated randomly by 0/1 invertible?

Suppose each entry of a $2\times 2$ matrix is populated with $0$ or $1$ independently with probability $1/2$. What is the probability that this matrix invertible? What will be the answer for a general $n\times n$ matrix? Thanks to @Anurag Sharma @Akshay Dhako Naik @SANDEEP R KASHYAP for asking this question?