Let A= [a_ i j ] be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability P ( E ) is :

Step-by-step solution

A= [a_y ]_ 2 2 and entries are 0 or 1. aligned & | array ll a & b c & d array |=0 & a d-b c=0 aligned Case I: a d=b c=1 a=b=c=d=1 Case II: a d=b c=0 array ll a=0, d=0 & b=0, c=0 a=0, d=1 & b=0, c=1 a=1, d=0 & b=1, c=0 array Total 10 cases when matrix is non invertible Total possible matrix =2^4=16 Required probability of invertible = 16-10 16 = 6 16 = 3 8