A good answer might be:
The transpose of a row matrix is a column matrix. And the transpose of a column matrix is a row matrix.
The transpose of a row matrix is a column matrix. And the transpose of a column matrix is a row matrix.
Here are some rules that cover what has been discussed. You should check that they seem reasonable, rather than memorize them. For each rule the matrices have the same number of rows and columns.
A + 0 = A A + B = B + A 0 + 0 = 0 A + (B + C) = (A + B) + C (ab)A = a(bA) a(A + B) = aB + aA a0 = 0 (-1)A = -A A - A= 0 (AT)T = A 0T = 0
In the above, a and b are scalars (real numbers). A and B are matrices, and 0 is the zero matrix of appropriate dimension.
If A = B and B = C, then does A = C?