MatricesMedium
Question
If A and B are square matrices of order 5 such that A2 + B4 = (AT)2, then det(B) is (where AT is transpose of matrix A) -
Options
A.0
B.1
C.2
D.0 or 1
Solution
A2 + B4 = (AT)2
(AT)2 + (BT)4 = A2
B4 = - (BT)4
|B|4 = |-B4|
|B|4 = -|B|4
|B| = 0
(AT)2 + (BT)4 = A2
B4 = - (BT)4
|B|4 = |-B4|
|B|4 = -|B|4
|B| = 0
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