Jika A^-1=[1 4 2 3]dan B=[-3 2 -2 1] maka A^-1.B^-1= ....

[[9, -14], [8, -13]]

Pembahasan

Untuk menyelesaikan soal ini, kita perlu melakukan perkalian matriks antara A^-1 dan B^-1.

A^-1 = [[1, 4], [2, 3]]
B = [[-3, 2], [-2, 1]]

Pertama, kita perlu mencari invers dari matriks B (B^-1).
Determinan B (det(B)) = (1 * -3) - (2 * -2) = -3 - (-4) = -3 + 4 = 1.

B^-1 = (1/det(B)) * [[1, -2], [2, -3]]
B^-1 = (1/1) * [[1, -2], [2, -3]]
B^-1 = [[1, -2], [2, -3]]

Sekarang kita dapat mengalikan A^-1 dengan B^-1:

A^-1 * B^-1 = [[1, 4], [2, 3]] * [[1, -2], [2, -3]]

Elemen pertama (baris 1, kolom 1) = (1*1) + (4*2) = 1 + 8 = 9
Elemen kedua (baris 1, kolom 2) = (1*-2) + (4*-3) = -2 + (-12) = -2 - 12 = -14
Elemen ketiga (baris 2, kolom 1) = (2*1) + (3*2) = 2 + 6 = 8
Elemen keempat (baris 2, kolom 2) = (2*-2) + (3*-3) = -4 + (-9) = -4 - 9 = -13

Maka, A^-1 * B^-1 = [[9, -14], [8, -13]]