Matrices Lecture 5

If A and B matrices commute then

Let P=[(2alpha),(5),(-3alpha^(2))] and Q=[(2l,-m,5n)] are two matrices, where l, m, n, alpha in R , then the value of determinant PQ is equal to

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 B are two square matrices of order 3xx3 which satify AB=A and BA=B , then (A+I)^(5) is equal to (where I is idensity matric)

If A and B are matrices of order 3 and |A|=5,|B|=3 , the |3AB|

Let A=[(3,-5),(7,-12)] and B=[(12,-5),(7,-3)] bc two given matrices, then (AB)^(-1) is :

If A and B are square matrices of order 3 such that |A|=5 and AB=-5I , then the value of |B| is

If A and B are symmetric matrices, then ABA is

If A and B are two matrices of order 3xx3 satisfying AB=A and BA=B , then (A+B)^(5) is equal to

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