A$.$ A confusion matrix is a matrix that shows the payoff of the predicted true positives $($TP$),$ false positives $($FP$),$ true negatives $($TN$),$ and false negatives $($FN$).$ The sum of the four quadrants

provides insight into the cumulative estimated payoff of the model at the given threshold value.

B$.$ The confusion matrix is basically a square matrix, whose all off$-$diagonal elements are zero and all on$-$diagonal elements are equal. In other words we can say that a confusion matrix is

basically a multiple of an identity matrix.

C$.$ A confusion matrix is a matrix that shows the predicted and actual classifications at a given threshold value. It identifies true positives $($TP$),$ false positives $($FP$),$ true negatives $($TN$),$ and

false negatives $($FN$)$ at the given threshold value.

D$.$ The confusion matrix is a tool to evaluate a model. It plots the false positive rate $($FP$)$ on the $x-$axis and the true positive rate $($TP$)$ on the $y-$axis. Comparing these two rates provides insight

into how well a model correctly identifies outcomes at any threshold value.