DeterminantHard
Question
Let A and B be two 2 × 2 matrix with real entries. If AB = O and tr(A) = tr(B) = 0 then
Options
A.A and B are comutative w.r.t. operation of multiplication.
B.A and B are not commutative w.r.t. operation of multiplication.
C.A and B are both null matrices.
D.BA = 0
Solution
Let A = 
and B = 
⇒ AB =
⇒ a1a2 + b1c2 = a1b2 - b1a2 = c1a2 - a1c2 = c1b2 + a1a2 = 0
BA =
and B = ⇒ AB =
⇒ a1a2 + b1c2 = a1b2 - b1a2 = c1a2 - a1c2 = c1b2 + a1a2 = 0
BA =
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