The concept of an identity matrix and inverse matrices, and determinants. Finding inverses with technology, or by hand for (2×2) matrices
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Practice exam-style identity, inverses & determinants problems
The identity matrix I is a square matrix with 1s along its top-left to bottom-right diagonal, and 0's everywhere else. When multiplied by any matrix with appropriate order, the product is the same matrix:
The inverse of a matrix is the matrix M−1 that when multiplied by M gives the identity.
If M=(acbd), then
A square matrix M is invertible if and only if its determinant is non-zero:
If the matrices A and B are invertible, then
You can find the inverse of any (square) matrix on your calculator. Enter your matrix into your calculator, for example in [A], and then simply type
and the calculator will spit out the inverse, if it exists.
You can find the determinant of any (square) matrix on your calculator.
Enter your matrix into your calculator, for example in [A].
Under the matrix menu, you will find a bunch of functions, the first of which should be det(. Type
and the calculator will spit out the determinant.