Let `A` be a matrix of order `3xx4` . If `R_1` denotes the first row of `A` and `C_2` denotes its second column, then determine the orders of matrices `R_1` and `C_2` .

Let A is a matrix of order 100xx 50 and B is matrix of order 50xx 75 and AB =C find the order of c

Let P be a matrix of order 3xx3 such that all the entries in P are from the set {-1,\ 0,\ 1} . Then, the maximum possible value of the determinant of P is ______.

If A is a square matrix of order 3 and A' denotes transpose of matrix A , A'.A^-1=I and det A=1 , then det (A^-1) must not equal to____ .

Let A be a square matrix of order 3 so that sum of elements of each row is 1 . Then the sum elements of matrix A^(2) is

In each of the following find r+s, r- s, rs, (r )/(s) if r denotes the first complex number and s denotes the second complex number 3i, 1-i

In each of the following find r+s, r- s, rs, (r )/(s) if r denotes the first complex number and s denotes the second complex number -7, -1-3i

Consider the set A of all matrices of order 3 xx 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1. Let C be the subset of A consisting of all matrices whose determinant is -1. Then which one of the following is correct ?