JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right]\). If \(M\) and \(N\) are two matrices given by \(M =\sum \limits_{ k =1}^{10} A ^{2 k }\) and \(N =\sum \limits_{ k =1}^{10} A ^{2 k -1}\) then \(MN ^{2}\) is
- A a non-identity symmetric matrix
- B skew symmetric matrix
- C neither symmetric nor skew-symmetric matrix
- D an identify matrix
Answer & Solution
Correct Answer
(A) a non-identity symmetric matrix
Step-by-step Solution
Detailed explanation
\(A =\left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right]\) \(A ^{2}=\left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right]\left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right]=\left[\begin{array}{cc}-4 & 0 \\ 0 & -4\end{array}\right]=-4 I\) \(A ^{3}=-4 A\)…
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