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If A=[[a,b],[c,d]] (where b c!=0 ) satis...

If `A=[[a,b],[c,d]]` (where `b c!=0` ) satisfies the equations `x^2+k=0,t h e n`

A

a + d = 0

B

`k=-abs(A)`

C

`k=abs(A)`

D

None of these

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the given matrix \( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) and the condition that it satisfies the equation \( x^2 + k = 0 \). This implies that \( A^2 + kI = 0 \), where \( I \) is the identity matrix. ### Step-by-Step Solution: 1. **Calculate \( A^2 \)**: \[ A^2 = A \cdot A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \cdot \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] ...
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