If A =[12-23], B= [2123] and C=[-3120]. Verify that (AB)C = A(BC) and A (B+C)=AB+AC

Answer 1

Let's calculate (AB)C:

AB = [12-23] * [2123] = [1212 - 2529] = [-1317]

Then, (AB)C = [-1317] * [-3120] = [4101840]

Now, let's calculate A(BC):

BC = [2123] * [-3120] = [-62376]

Then, A(BC) = [12-23] * [-62376] = [1212 + 71712] = [72924]

Since [4101840] = [72924], we have verified that (AB)C = A(BC).

Now, let's calculate A(B+C):

B + C = [2123] + [-3120] = [-1007]

Then, A(B+C) = [12-23] * [-1007] = [1212 + 24284] = [25596]

Now, let's calculate AB + AC:

AB = [12-23] * [2123] = [1212 - 2529] = [-1317]
AC = [12-23] * [-3120] = [1212 + 71712] = [72924]
AB + AC = [-1317] + [72924] = [71607]

Since [25596] = [71607], we have verified that A(B+C) = AB + AC.

Therefore, we have verified the equations (AB)C = A(BC) and A(B+C) = AB + AC.