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Since our matrix A A A has a determinant which is not equal to zero, we can determine A A A is an invertible matrix and so, we can finally calculate its inverse. The first part of our proof is to verify this matrix is in fact an invertible matrix, for that, we obtain its determinant: For that we define matrix A A A as shown below: On this section we will prove how a 2x2 matrix and its inverse meet the condition defined in equation 2. Later, in our last section, we will work through a series of exercises in order for you to practice.
INVERSE OF 2X2 MATRIX HOW TO
Having learnt the usage and how to get the inverse of a 2x2 matrix, let us go next into a section dedicated to prove that equations 2 and 5 are correct, if other words, let us calculate the inverse of 2x2 matrix proof with an example given matrix so you can observe the formula for inverse of 2x2 matrix in action. And so, we can conclude that B B B is equal to the inverse of A A A time C C C. Then, applying what we learnt in our lesson about the identity matrix, we know that any matrix multiplied by an identity matrix gives a result the non-identity matrix itself. In general, the condition of invertibility for a nxn matrix A A A is:Ī ⋅ A − 1 = A − 1 A ⋅ A = I n A \cdot A^ I n of the same dimensions as the original matrices. In other words, an invertible matrix is that which has an inverse matrix related to it, and if both of them (the matrix and its inverse) are multiplied together (no matter in which order), the result will be an identity matrix of the same order. In our past lesson we learnt that for an invertible matrix there is always another matrix which multiplied to the first, will produce the identity matrix of the same dimensions as them.