Determinants and Inverses

Front

What is a multiplicative inverse?

Back

A multiplicative inverse of a number or matrix is another number or matrix which, when multiplied together, results in the identity element (1 for numbers, and the identity matrix for matrices).

Front

What is a square matrix?

Back

A square matrix is a matrix that has the same number of rows and columns.

Front

How do you determine if two matrices are multiplicative inverses?

Back

Two matrices A and B are multiplicative inverses if the product AB equals the identity matrix.

Front

What is the determinant of a 2x2 matrix [[a, b], [c, d]]?

Back

The determinant is calculated as ad - bc.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Front

What is the determinant of a 3x3 matrix?

Back

The determinant of a 3x3 matrix can be calculated using the rule of Sarrus or cofactor expansion.

Front

What does a determinant of zero indicate about a matrix?

Back

A determinant of zero indicates that the matrix is singular, meaning it does not have an inverse.

Front

What is the formula for the determinant of a 2x2 matrix?

Back

For a matrix [[a, b], [c, d]], the determinant is ad - bc.

Front

What is the relationship between determinants and matrix inverses?

Back

If a matrix has a non-zero determinant, it has an inverse; if the determinant is zero, the matrix does not have an inverse.

Front

How can you evaluate the determinant of a matrix using row operations?

Back

You can use row operations to simplify the matrix to an upper triangular form, then multiply the diagonal elements to find the determinant.