ee.Image.arrayDimensions

// A function to print arrays for a selected pixel in the following examples.
function sampArrImg(arrImg) {
  var point = ee.Geometry.Point([-121, 42]);
  return arrImg.sample(point, 500).first().get('array');
}

// A 3-band image of constants.
var img = ee.Image([0, 1, 2]);
print('3-band image', img);

// Convert the 3-band image to a 2D array image.
var arrayImg2D = img.toArray().toArray(1);
print('2D array image (pixel)', sampArrImg(arrayImg2D));
// [[0],
//  [1],
//  [2]]

// Get the number of dimensions in each pixel's array.
var arrayImg2Ddim = arrayImg2D.arrayDimensions();
print('N dimensions in array', sampArrImg(arrayImg2Ddim));
// 2

// Get the array length per dimension per pixel.
var arrayImg2DdimLen = arrayImg2D.arrayLengths();
print('Array length per dimension', sampArrImg(arrayImg2DdimLen));
// [3, 1]

// Get the array length for 0-axis (rows).
var arrayImg2Daxis0Len = arrayImg2D.arrayLength(0);
print('Array length 0-axis (rows)', sampArrImg(arrayImg2Daxis0Len));
// 3

// Get the array length for 1-axis (columns).
var arrayImg2Daxis1Len = arrayImg2D.arrayLength(1);
print('Array length 1-axis (columns)', sampArrImg(arrayImg2Daxis1Len));
// 1

# A function to print arrays for a selected pixel in the following examples.
def samp_arr_img(arr_img):
  point = ee.Geometry.Point([-121, 42])
  return arr_img.sample(point, 500).first().get('array')

# A 3-band image of constants.
img = ee.Image([0, 1, 2])
print('3-band image:', img.getInfo())

# Convert the 3-band image to a 2D array image.
array_img_2d = img.toArray().toArray(1)
print('2D array image (pixel):', samp_arr_img(array_img_2d).getInfo())
# [[0],
#  [1],
#  [2]]

# Get the number of dimensions in each pixel's array.
array_img_2d_dim = array_img_2d.arrayDimensions()
print('N dimensions in array:', samp_arr_img(array_img_2d_dim).getInfo())
# 2

# Get the array length per dimension per pixel.
array_img_2d_dim_len = array_img_2d.arrayLengths()
print(
    'Array length per dimension:',
    samp_arr_img(array_img_2d_dim_len).getInfo()
)
# [3, 1]

# Get the array length for 0-axis (rows).
array_img_2d_axis0_len = array_img_2d.arrayLength(0)
print(
    'Array length 0-axis (rows):',
    samp_arr_img(array_img_2d_axis0_len).getInfo()
)
# 3

# Get the array length for 1-axis (columns).
array_img_2d_axis1_len = array_img_2d.arrayLength(1)
print(
    'Array length 1-axis (columns):',
    samp_arr_img(array_img_2d_axis1_len).getInfo()
)
# 1