Dengan menggunakan matriks persegi, tunjukkan bahwa (B^-1)^-1=B
dan [B^t]^-1=[B^-1]^t
Jawaban Terkonfirmasi
A)
misalkan matik B = (1 3)
(2 4)
(B^-1)^-1 = B
B^-1 = 1/-2 (4 -3)
(-2 1)
= (-2 3/2)
(1 -1/2)
(B^-1)^-1 = -2 ( -1/2 -3/2)
( -1 -2)
= (1 3)
(2 4)
terbukti bahwa (b^-1)^-1 = B
b)
B^t = (1 2)
(3 4)
(B^t)^-1 = 1/-2 (4 -2)
(-3 1)
= (-2 1)
(3/2 -1/2)
(B^-1)^t = (-2 1)
(3/2 -1/2)
terbukti bahwa (B^t)^-1 = (B^-1)^t