Is the matrix bmatrix 4 & 6 \\ 2 & 3 bmatrix invertible?

A square matrix is invertible exactly when its determinant is not zero. The determinant is $(4)(3)-(6)(2)=12-12=0$, so the matrix is not invertible, choice D. You can also notice that the first row is twice the second row, so the rows are dependent. Choice A claims a nonzero determinant, which is false. Choice B is wrong because the matrix is square ($2\times2$). Choice C is wrong because positive entries do not guarantee invertibility, as this example shows. The determinant is the test.