If M and N are square matrices of order 3, th | vedclass

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(C) For two square matrices $M$ and $N$ of order $3$: $1$. The matrix $MN - NM$ is skew-symmetric if $M$ and $N$ are symmetric matrices, because $(MN

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For all symmetric matrices $M$ and $N$, matrix $MN$ is symmetric

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(C) For two square matrices $M$ and $N$ of order $3$: $1$. The matrix $MN - NM$ is skew-symmetric if $M$ and $N$ are symmetric matrices, because $(MN - NM)^T = (MN)^T - (NM)^T = N^T M^T - M^T N^T = NM - MN = -(MN - NM)$. $2$. The matrix $N^T MN$ is symmetric or skew-symmetric according as $M$ is symmetric or skew-symmetric, because $(N^T MN)^T = N^T M^T (N^T)^T = N^T M^T N$. If $M^T = M$, then $(N^T MN)^T = N^T MN$ (symmetric). If $M^T = -M$, then $(N^T MN)^T = -N^T MN$ (skew-symmetric). $3$. The product of two symmetric matrices $MN$ is symmetric if and only if $MN = NM$. Since this is not true for all symmetric matrices, statement $(c)$ is false. $4$. For any two matrices $M$ and $N$, $	ext{adj}(MN)$ and $	ext{adj}(NM)$ are not necessarily equal. Thus, the statement that is not true is $(c)$.

If $M$ and $N$ are square matrices of order $3$, then which one of the following statements is not true?

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