Matrices Q&A 3: How to Find the Inverse of a Matrix and Verify with Identity Matrix

Hello everyone,
It’s another amazing day with Mathematics! In today’s session, we are given a 2x2 matrix and tasked with finding its inverse. We’re also required to verify whether the product of matrix A and the inverse of A results in an identity matrix.

The first step I took was to find the inverse of the matrix. To do this, I recalled the formula:
A⁻¹ = (1/det(A)) × adj(A).

So I began by calculating the determinant of matrix A, followed by obtaining the adjoint of matrix A. After finding both matrices, I substituted them into the inverse formula, which resulted in a scalar multiplication involving the adjoint matrix.

Next, I simplified the expression by applying the scalar multiplication rule, and that gave us the inverse of matrix A.
With the inverse now available, I proceeded to verify the second part of the question; whether multiplying matrix A by its inverse would give us the identity matrix. This step involved matrix multiplication. I carefully followed the rules of matrix multiplication and, after completing the operation, the result was indeed an identity matrix.

This confirms that the inverse was correctly calculated, and that multiplying a matrix by its inverse produces the identity matrix, as expected.
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