Matrix Multiplication Warmup

Front

What is matrix multiplication?

Back

Matrix multiplication is a binary operation that produces a matrix from two matrices. The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

How do you determine the size of the product of two matrices?

Back

If matrix A is of size m x n and matrix B is of size n x p, then the product AB will be of size m x p.

Front

What is the formula for multiplying two matrices?

Back

The element in the i-th row and j-th column of the product matrix is calculated as the dot product of the i-th row of the first matrix and the j-th column of the second matrix.

Front

Can you multiply a 2x3 matrix with a 3x2 matrix?

Back

Yes, you can multiply a 2x3 matrix with a 3x2 matrix. The resulting matrix will be of size 2x2.

Front

What is the result of multiplying a matrix by the identity matrix?

Back

Multiplying any matrix by the identity matrix of appropriate size leaves the original matrix unchanged.

Front

What is the commutative property of matrix multiplication?

Back

Matrix multiplication is not commutative; that is, AB does not necessarily equal BA.

Front

What is the associative property of matrix multiplication?

Back

Matrix multiplication is associative; that is, (AB)C = A(BC) for any compatible matrices A, B, and C.

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero. It acts as the additive identity in matrix addition.

Front

What is a transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows and columns. If A is an m x n matrix, then its transpose A^T is an n x m matrix.

Front

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

Back

For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as ad - bc.