Matrices Review

A matrix is a rectangular array of numbers arranged in rows and columns.

The determinant is calculated as det(A) = ad - bc.

The inverse is given by A⁻¹ = (1/det(A)) * ⌈d & -b⌉
⌊-c & a⌋, provided det(A) ≠ 0.

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

The product of two matrices is obtained by multiplying rows of the first matrix by columns of the second matrix.

Two matrices A and B are multiplicative inverses if AB = I, where I is the identity matrix.

A zero matrix is a matrix in which all elements are zero.

You add two matrices by adding their corresponding elements.

Scalar multiplication involves multiplying each element of a matrix by a scalar (a constant number).

The transpose of a matrix is obtained by swapping its rows and columns.