The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by \( ad - bc \). Here, \( 1*4 - 2*3 = 4 - 6 = -2 \).

The determinant of a diagonal matrix is the product of its diagonal elements: \( 5*7 = 35 \).

The determinant is calculated as \( 5*8 - 6*7 = 40 - 42 = -2 \).

The determinant of an upper triangular matrix is the product of its diagonal elements: \( 1*1*1 = 1 \).

Using the determinant formula for 3x3 matrices, we find \( 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1 \).

The determinant is 0 because the rows are linearly dependent.

The determinant is calculated as \( 2*7 - 5*3 = 14 - 15 = -1 \).

The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).

The determinant of the identity matrix is always 1.

The determinant of this matrix is 0 because the rows are linearly dependent.

The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).

Determinant of H = (3*5) - (2*1) = 15 - 2 = 13.

Determinant of B = (2*7) - (3*5) = 14 - 15 = -1.

Determinant of B = (5*3) - (1*2) = 15 - 2 = 13.

The determinant is calculated as \( 2*4 - 1*3 = 8 - 3 = 5 \).

The determinant is \( 0*0 - 1*1 = 0 - 1 = -1 \).

The determinant of the identity matrix is always 1.