Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have to matrices:

$$A=\pmatrix{1&a&1\\1&0&a\\1&2&0} ; \quad B= \pmatrix{1&b&3\\2&1&0}$$

The task is to determine $AB, AB^T, BA$

I think i cannot calculate the matrix of $AB$ because $\text{Columns} \ A = 3$ is not $\text{Rows} \ B = 2$

But i can calculate $BA$:


Now my question is, what is meant with $ AB^T$ ? Thanks

share|cite|improve this question
Do you know what $B^T$ is? – Git Gud Jun 29 '14 at 10:47
@GitGud no i dont know – John Smith Jun 29 '14 at 10:48
The superscript $T$ denotes the matrix transpose. Basically it's a new matrix whose $i^{\text{th}}$ column is the $i^{\text{th}}$ line of the original matrix. – Git Gud Jun 29 '14 at 10:50
John, you may use \text{anything} for writing text in LaTeX. [TeX TIP] – Kushashwa Ravi Shrimali Jun 29 '14 at 10:52
Perhaps you should understand what transpose of a matrix is first! – pushpen.paul Jun 29 '14 at 14:32
up vote 2 down vote accepted

$A\times B^T$ means the matrix $A$ multiplied by the transpose of $B$. Given some matrix $A$, the transpose, $A^T$, is a matrix such that the columns of $A$ are the rows of $A^T$ and the rows of $A$ are the columns of $A^T$. Thus we see that $$B^T= \left(\begin{matrix} 1 & 2 \\ b & 1 \\ 3 & 0 \\ \end{matrix}\right) .$$ You can now evaluate $A\times B^T.$

share|cite|improve this answer

Hint: $B^{T}$ means transpose of $B$. You can read about transpose here.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.