$8 I$
$5 I$
Given \(A^2 = I\), the identity matrix, we analyze \((I + A)^4\):
\[(I + A)^2 = I^2 + 2IA + A^2 = I + 2A + I = 2I + 2A\]
\[(I + A)^4 = ((I + A)^2)^2 = (2I + 2A)^2\]
Expanding \((2I + 2A)^2\):
\[(2I + 2A)^2 = 4I^2 + 8IA + 4A^2\]
Since \(A^2 = I\), substitute \(4A^2 = 4I\):
\[(2I + 2A)^2 = 4I + 8A + 4I = 8I + 8A\]
Now compute \((I + A)^4 - 8A\):
\[(I + A)^4 - 8A = (8I + 8A) - 8A = 8I\]
Thus, the result is: \[8I\]
List-I (Name of account to be debited or credited, when shares are forfeited) | List-II (Amount to be debited or credited) |
---|---|
(A) Share Capital Account | (I) Debited with amount not received |
(B) Share Forfeited Account | (II) Credited with amount not received |
(C) Calls-in-arrears Account | (III) Credited with amount received towards share capital |
(D) Securities Premium Account | (IV) Debited with amount called up |