Matrices Lecture 1

If A and B matrices commute then

Seven different lecturers are to deliver lectures in seven perday. A, B and C are three oftne lectures. The number of ways in which a routine for theday canr be made such that A delivers his lecture before B and B before C, is

If A and P are the square matrices of the same order and if P be invertible, show that the matrices A and P^(-1) have the same characteristic roots.

If A, B, C are invertible matrices, then (ABC)^(-1) =

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 ?

If [(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C , where A, B and C are matrices then find matrices B and C.

Show that the following matrices are skew symmetric: [[0,1,-1],[-1,0,1],[1,-1,0]]

Which of the following matrices is equal to 4[(-1,2),(0,-4)] ?

If A; B are invertible matrices of the same order; then show that (AB)^-1 = B^-1 A^-1

If A and B are symmetric matrices, then ABA is