Matrix Transpose:

If A = [aᵢⱼ] then Aᵀ = [aⱼᵢ]

Rows become columns

Symmetric Matrix:

Aᵀ = A

Example: A = [[1, 2], [2, 3]]

Skew-Symmetric:

Aᵀ = -A

Diagonal elements are zero

Determinant (2×2):

|A| = ad – bc for A = [[a, b], [c, d]]

Determinant (3×3):

|A| = a(ei – fh) – b(di – fg) + c(dh – eg)

for A = [[a, b, c], [d, e, f], [g, h, i]]