Consider the set X of all 2 × 2 matrices with matrix entries 1 or 2. The probability of a set of matrices Y with some property is the number of matrices in Y divided by the number of matrices in X. What is the probability that the rank of the matrix is 0? 1? 2?
So, there are 16 total possible 2x2 matrices. The rank of a matrix is the # of leading 1s-- so, for the first question, would this be (1)/(16)? There is only 1 possible matrices with leading 1s (all 1s)?