Linear Algebra · Lesson 6
Inverse Matrices
The inverse of a matrix A is another matrix A⁻¹ such that A·A⁻¹ = I. It "undoes" the transformation encoded by A — the matrix equivalent of dividing by a number.
Quick Check
1. A matrix has an inverse only when:
It is symmetric
Its determinant is non-zero
It is a square matrix with all positive entries
det = 1
2. For A = [[2, 0], [0, 3]], what is A⁻¹?
[[2, 0],[0, 3]]
[[1/2, 0],[0, 1/3]]
[[3, 0],[0, 2]]
[[−2, 0],[0, −3]]
3. (AB)⁻¹ equals:
A⁻¹B⁻¹
B⁻¹A⁻¹
(BA)⁻¹
A⁻¹+B⁻¹
4. If det(A) = 4, then det(A⁻¹) = ?
4
1/4
−4
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