If $\mathbf{A}$ and $\mathbf{B}$ are both non-singular $\mathrm{n} \times \mathrm{n}$ matrices, then which of the following statement is NOT TRUE. Note: det represents the determinant of a matrix.
(A) $\operatorname{det}(\mathbf{A B})=\operatorname{det}(\mathbf{A}) \operatorname{det}(\mathbf{B})$
(B) $\operatorname{det}(\mathbf{A}+\mathbf{B})=\operatorname{det}(\mathbf{A})+\operatorname{det}(\mathbf{B})$
(C) $\operatorname{det}\left(\mathbf{A} \mathbf{A}^{-1}\right)=1$
(D) $\operatorname{det}\left(\mathbf{A}^{\mathrm{T}}\right)=\operatorname{det}(\mathbf{A})$

Question ID - 155634 | SaraNextGen Top Answer

If $\mathbf{A}$ and $\mathbf{B}$ are both non-singular $\mathrm{n} \times \mathrm{n}$ matrices, then which of the following statement is NOT TRUE. Note: det represents the determinant of a matrix.
(A) $\operatorname{det}(\mathbf{A B})=\operatorname{det}(\mathbf{A}) \operatorname{det}(\mathbf{B})$
(B) $\operatorname{det}(\mathbf{A}+\mathbf{B})=\operatorname{det}(\mathbf{A})+\operatorname{det}(\mathbf{B})$
(C) $\operatorname{det}\left(\mathbf{A} \mathbf{A}^{-1}\right)=1$
(D) $\operatorname{det}\left(\mathbf{A}^{\mathrm{T}}\right)=\operatorname{det}(\mathbf{A})$