Q18Multiple correct3 Marks27 Oct 2024

Choose the correct option(s) from the following:

A

Let $A,B\in M_{n\times n}(\mathbb{R})$ such that $AB=0$. Then at least one of the matrices $A$ or $B$ must have determinant $0$.

B

If $A-\alpha I=0$ where $A\in M_{n\times n}(\mathbb{R})$, $I$ is the identity matrix of order $n$, $\alpha\in\mathbb{R}$ and $n$ is even, then determinant of $A$ is always positive.

C

A matrix with all diagonal entries as zero will always have determinant zero.

D

For a square matrix $A$, if the system of linear equations $Ax=0$ has a unique solution, then determinant of $A$ is non-zero.