Elementary mathematics-matrix

Question

Elementary Mathematics

1. Let and c=3 ,d=5 then verify the formula 

a) (A+B)^t=A^t=B^t

b)c(A+B)=c.A+c.B

c)(c+d).A=c.A+d.A

2. Show the matrix is a singular matrix

3. Calculate the inverse of 

4. Calculate the determinant of the given matrices  

5. A) Let  and  then calculate  (i.e. matrix multiplication.

B) Let and then calculate A,B,A+B,A-B.

7. a)Let than verify det(A^T)=det(A) and

b) Letand then verify det(AB)=det(A).det(B)