The number of 2 `x` 2 matrices A such that all entries are either 1 or 0 is

The number of 3xx3 matrices A whose entries are either 0 or 1 and for which the system A[[xyz]]=[[00]] has exactly two distinct solution is a.0 b.2^(9)-1 c.168 d.2

Let A = [[0,1,0],[1,0,0],[0,0,1]] . Then the number of 3 xx 3 matrices B with entries from the set {1, 2, 3, 4, 5} and satisfying AB = BA is _______.

The number of 2xx2 matrices A with real entries, such that A+A^(T)=3I and A A^(T)=5I , is equal to

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

The total number of 3 xx 3 matrices A having entries from the set {0,1,2,3} such that the sum of all the diagonal entries A ^(T)A is 9, is equal to "________"

The number of all 3times3 matrices A ,with entries from the set {-1,0,1} such that the sum of the diagonal elements of A A^(T) is 3 ,is k then (k)/(10) is