Solution
= Solution
The <elementary row operations> preserve the <determinant>, and the diagonal product of the <upper triangular matrix> found above is
$$
\det B=(1-t^2)^3.
$$
Consequently
$$
\boxed{B\text{ is not invertible exactly when }t=1\text{ or }t=-1.}
$$
At $t=1$, all four rows are equal. At $t=-1$, successive rows alternate between one row and its negative. In either case the <matrix rank> is one, confirming the vanishing <determinant>.