Let
$A=\left[\begin{matrix}\cos \theta &\sin \theta \\ -\sin \theta &\cos \theta \end{matrix}\right] $
Consider the following statements:
Statement-l: If X is an nn matrix, then det(mX) = $m ^ n$ det(X), where m is a scalar.
Statement-II: If Y is a matrix obtained from X by multiplying any row or column by a scalar m, then det (Y) = m det (X).
Which one of the following is correct in respect of the above statements?
Consider the following statements about
the matrix $M=\left[\begin{matrix}71&23&48\\ 57&28&29\\ 65&17&48\end{matrix}\right]$
Statement-I: The inverse of M does not exist.
Statement-II: M is non-singular.
Which one of the following is correct in respect of the above statements?
If $\Delta = \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} $
and A, B, C, D, G are the cofactors of the elements a, b, c, d, g respectively, then what is equal to?
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