Matrix Inverses Quiz

What is the main characteristic of an identity matrix?

• It has all elements as zero.

• It has ones on the main diagonal and zeros elsewhere.

• It is always a 2x2 matrix.

• It has equal numbers of rows and columns, but no specific pattern.

What happens when you multiply any matrix by an identity matrix?

• You get the original matrix back.

• The matrix becomes a scalar.

• You get a zero matrix.

• The matrix becomes a diagonal matrix.

Under what condition does a 2x2 matrix have an inverse?

• When it has more rows than columns.

• When its determinant is not zero.

• When it is a square matrix.

• When its determinant is zero.

How do you find the inverse of a 2x2 matrix?

• By swapping the rows and columns.

• By multiplying each element by the determinant.

• By switching the main diagonal elements and changing the signs of the other diagonal.

• By adding the identity matrix to it.

What is the result of multiplying a matrix by its inverse?

• A zero matrix.

• The identity matrix.

• A scalar multiple of the original matrix.

• A matrix with all elements as one.

What is the determinant of the matrix used in the example?

• Zero

• Fourteen

• One

• Fifteen

Why can't a matrix with a determinant of zero have an inverse?

• Because it is not a square matrix.

• Because it would involve division by zero.

• Because it is already an identity matrix.

• Because it has more columns than rows.

What is a necessary condition for a matrix to have an inverse?

• It must have a determinant of zero.

• It must have more rows than columns.

• It must be a non-square matrix.

• It must be a square matrix.

What advanced method can be used to find the inverse of larger matrices?

• Matrix subtraction

• Column addition

• Row transformations

• Determinant scaling

What is the inverse of a matrix with a determinant of 20?

• An identity matrix.

• A zero matrix.

• 20 times the matrix with switched diagonals and signs.

• 1/20 times the matrix with switched diagonals and signs.