If $\mathrm{M,N}$ are $3\times 2, 2 \times 3$ matrices such that $\mathrm{MN}=$ is given. Then $\mathrm{det(NM)}$ is?

Hint If $p \geq q$ and $M, N$ are $p \times q$ and $q \times p$ matrices, respectively, then the characteristic polynomials of $p, q$ are related by $$ p_{MN}(\lambda) = \lambda^{p - q} p_{NM}(\lambda) . $$

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Linear Algebra

Matrices

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