a) Letters of the English alphabet symmetric about a vertical mirror are: -

A, H, I, M, O, U, V, W, X and Y

These letters when flipped horizontally along a mirror retains the original figure which is shown as follows:

b) Letters of the English alphabet symmetric about a horizontal mirror: -

B, C, D, E, H, I, O and X

The letters when flipped vertically along a mirror retains the original figure which is shown as follows:

c) Letters of the English alphabet symmetric about both horizontal and vertical mirrors: -

H, I, O and X

The letters when flipped along both the axes (horizontal and vertical) retains the original figure.