1838.sagews

a=matrix(2,2,(1,5,-1,2));a  #initialize a 2x2 matrix

[ 1 5] [-1 2]

b=matrix(2,2,(-2,1,1,1));b  #initialize a 2x2 matrix

[-2 1] [ 1 1]

c=a+b;c  #find a matrix sum

[-1 6] [ 0 3]

d=b-a;d  #find a matrix difference

[-3 -4] [ 2 -1]

e=a*b;e  #show matrix products are not commutative

[3 6] [4 1]

f=b*a;f  #show matrix products are not commutative

[-3 -8] [ 0 7]

g=a**2;g  #square a matrix

[-4 15] [-3 -1]

h=b**3;h  #cube a matrix

[-11 4] [ 4 1]

i=a^(-1);i   #find the inverse of a matrix

[ 2/7 -5/7] [ 1/7 1/7]

j=b**(-1);j.n()  #find the inverse of a matrix

[-0.333333333333333 0.333333333333333] [ 0.333333333333333 0.666666666666667]

k=det(a);k  #find the determinant of a matrix

7

l=b.det();l  #find the determinant of a matrix

-3