https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:intro-to-matrix-inverses/v/inverse-matrix-introduction 2022-10-07T00:22:18.752150461Z Inverse matrix introduction The inverse of a square matrix is another matrix (of the same dimensions), where the multiplication (or composition) of the two matrices results in the identity matrix. This is analogous to inverse functions (if we think of matrices as functions) or reciprocal numbers (if we think of matrices as special numbers). Fascinating! Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/46507355-1c87-4186-b9f6-e16ee5721ffa_1280_720_base.png Inverse matrix introduction The inverse of a square matrix is another matrix (of the same dimensions), where the multiplication (or composition) of the two matrices results in the identity matrix. This is analogous to inverse functions (if we think of matrices as functions) or reciprocal numbers (if we think of matrices as special numbers). Fascinating! https://cdn.kastatic.org/ka-youtube-converted/sT9IgHjjhiY.mp4/sT9IgHjjhiY.mp4 410 Introduction to matrix inverses https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:intro-to-matrix-inverses/v/invertible-matrices-and-determinants 2022-10-07T00:22:18.752150461Z Invertible matrices and determinants An invertible matrix is a matrix that has an inverse. In this video, we investigate the relationship between a matrix's determinant, and whether that matrix is invertible. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/bf684400-4638-4047-af06-11ec9bf64ea2_1280_720_base.png Invertible matrices and determinants An invertible matrix is a matrix that has an inverse. In this video, we investigate the relationship between a matrix's determinant, and whether that matrix is invertible. https://cdn.kastatic.org/ka-youtube-converted/GuFvSwriy1Q.mp4/GuFvSwriy1Q.mp4 282 Introduction to matrix inverses https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:intro-to-matrix-inverses/v/invertible-matrices-and-transformations 2022-10-07T00:22:18.752150461Z Invertible matrices and transformations An invertible matrix is a matrix that has an inverse. In this video, we compare the effect of two transformations, one defined by an invertible matrix and one by a non-invertible matrix. We see that the non-invertible matrix map the entire plane onto a single line. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/2187428c-3d85-462c-ae6a-60ba93fc7777_1280_720_base.png Invertible matrices and transformations An invertible matrix is a matrix that has an inverse. In this video, we compare the effect of two transformations, one defined by an invertible matrix and one by a non-invertible matrix. We see that the non-invertible matrix map the entire plane onto a single line. https://cdn.kastatic.org/ka-youtube-converted/S278zOWSsZM.mp4/S278zOWSsZM.mp4 368 Introduction to matrix inverses https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:intro-to-matrix-inverses/v/inverse-matrices-and-matrix-equations 2022-10-07T00:22:18.752150461Z Inverse matrices and matrix equations In other videos, we've seen how matrices can represent systems of equations, and we've also seen how matrices whose determinant is zero don't have an inverse. In this video, we connect this two understanding, and by doing that way we understand how we can solve systems of equations with matrices. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/70d33dec-6fad-4ad4-932c-25db18e5d102_1280_720_base.png Inverse matrices and matrix equations In other videos, we've seen how matrices can represent systems of equations, and we've also seen how matrices whose determinant is zero don't have an inverse. In this video, we connect this two understanding, and by doing that way we understand how we can solve systems of equations with matrices. https://cdn.kastatic.org/ka-youtube-converted/a2S0kuXO3gE.mp4/a2S0kuXO3gE.mp4 450 Introduction to matrix inverses https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:intro-to-matrix-inverses/e/determine-invertibile-2x2-matrices 2025-05-05T08:14:25.350149109Z Determine invertible matrices Determine whether a 2x2 matrix has an inverse by either thinking about its determinant or about its effect on the unit square. Tomer Gal exercise