Question

If A is an n× n matrix, then det A = det AT . Verify this theorem for 2 × 2 matrices.

Answer 1

Verified

Explanation:

Let A matrix be in the form of

`\left[\begin{array}{cc}a&b\\c&d\end{array}\right]`

Then det(A) = ad - bc

Matrix A transposed would be in the form of:

`\left[\begin{array}{cc}a&c\\b&d\end{array}\right]`

Where we can also calculate its determinant:

det(AT) = ad - bc = det(A)

So the determinant of the nxn matrix is the same as its transposed version for 2x2 matrices