Functions Involving Parameters, Vectors, and Matrices

-16

+16

+4

-4

The value of the determinant doubles.

The sign of the determinant changes.

The value of the determinant remains unchanged.

The absolute value increases by one unit.

$ad - bc$

$abcd$

$ab + cd$

$a^2 - d^2$

By finding the determinant of the submatrix that remains after removing the row and column containing that element.

Dividing the determinant of the whole matrix by the element.

Multiplying the element by its cofactor.

Adding all other elements except for those in the same row or column.

Zero.

Not zero.

Greater than one.

Less than one.

AB is the determinant of A.

AI is the identity matrix B.

B is the inverse of A.

The determinant of B is zero.

$ad - bc$

$\frac{a}{b} + \frac{c}{d}$

$\frac{a + d}{b + c}$

$ab + cd$

Commutative Property

Identity Property

Associative Property

Distributive Property

2

10

-10

6

They must both be square matrices.

They must have the same determinant value.

They must have the same number of rows.

They have dimensions such that the number of columns in the first matrix matches the number of rows in the second.