This document contains the solutions to 3 exercises: 1) Finding the products of a matrix A and the identity matrix I. It is shown that AI = IA = A. 2) Finding the products of matrices A and B, and B and A. It is shown that in general, AB ≠ BA. 3) Determining if the product of matrices A and B is equal to the inverse of A.

1. 16 de agosto de 2012
Asignación II
Darvin Colón K00291438
Eric J. Burgos E00348857
Ejercicios 1
A = (
2 3
4 −1
) I = (
0 0
0 0
)
a) I(A) b) A(I) c) A(I) = I(A)
a) (
1(2) + 0(4)
0(2) + 1(4)
) (
1(3) + 0(−1)
0(3) + 1(−1)
) = (
2 + 0
0 + 4
) (
3 + 0
0 + 0
) = (
2 3
4 −1
)
b) (
2(1) + 3(0)
4(1) + − 1(0)
) (
2(0) + 3(1)
4(0) + − 1(1)
) = (
2 + 0
0 + 4
) (
0 + 3
0 + − 1
) = (
2 3
4 −1
)
c) I = A
Ejercicio 2
A = (
−3 0
4 5
) B = (
7 −1
8 0
)
a) AB b) BA c) AB = BA
a) (
−3(7) + 0(8)
4(7) + 5(8)
) (
−3(−1) + 0(8)
4(−1) + 5(0)
) = (
−21 + 0
28 + 40
) (
3 + 0
−4 + 0
) = (
−21 −3
68 −4
)
b) (
7(−3) + − 1(4)
8(−3) + 0(4)
) (
7(0) + − 1(5)
8(0) + 0(5)
) = (
−21 + − 4
−24 + 0
) (
0 + − 5
0 + 0
) =
(
−25 + − 5
−24 + 0
)
c) AB no = BA

2. Ejercicio 3
A = (
7 2
5 4
) B = (
4/18 −2/18
−5/18 7/18
)
Determinar si AB = A^-1