If , then verify that A’ A = I

Question

If , then verify that A A = I
Matrix A is a 2x2 matrix with elements [[cos alpha, sin alpha], [-sin alpha, cos alpha]].

Philoid · Accepted Answer

We know A’ can be calculated by taking the transpose of the given matrix A.

Now multiply A and A’. So,

And we know ‘I’ represents an identity matrix

From equation 1 & 2 we can say that

AA’ = I

AA’ = I. Hence verified.