Mathematics - Matrices Question with Solution | TestHub

Let $A={\left[a_{ij}\right]}_{4\times 3}$ and $B={\left[b_{ij}\right]}_{3\times 4}$ then $\det (AB)$ is always 0 .

If A and B are non-zero square matrices of same order such that $\mathrm{AB}=0$, then the value of $|A|+|B|+5$ is equal to 5

Let A be and $3\times 3$ orthogonal matrix such that $\mathrm{AB}=\mathrm{BA}$, then $\left|A{B}^T-B^{T}A+2I\right|$ is equal to $3^2$

Let A and B be square matrices of order $3\times 3$ such that $|A|=1$ and $|B|=3$, then the value of $\left|2A^2(B^{-1}{)}^3\right|$ is equal to $8/9$