Let `M=[[a,-360],[b,c]],` where `a,b` and `c` are integers.Find the smallest positive value of `b` such that `M^(2)=0`, where `O` denotes `2times2` null matrix.

If 97/19 = a+ 1/(b+1/c) where a, b and c are positive integers, then what is the sum of a, b and c?

Let P be a non - singular matrix such that I+P+P^(2)+…….P^(n)=O (where O denotes the null matrix), then P^(-1) is

Let A=[(1,0,3),(0,b,5),(-(1)/(3),0,c)] , where a, b, c are positive integers. If tr(A)=7 , then the greatest value of |A| is (where tr (A) denotes the trace of matric A i.e. the sum of principal diagonal elements of matrix A)

Let A be a 2 xx 2 matrix of the form A = [[a,b],[1,1]] , where a, b are integers and -50 le b le 50 . The number of such matrices A such that A^(-1) , the inverse of A, exists and A^(-1) contains only integer entries is

If a^(b^(t))=6561 ,then find the least possible value of (a.b.c), where a,b and c are integers.

Let A and B be two square matrices of order 3 and AB = O_(3) , where O_(3) denotes the null matrix of order 3. then

Find the minimum value of ax+by, where xy=c^(2) and a,b,c are positive.