Can a regular square matrix times any matrix of the same size equal zero?

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- Nov 1st 2010, 09:23 AMjayshizwizMatrix Multiplication question
Can a regular square matrix times any matrix of the same size equal zero?

- Nov 1st 2010, 09:30 AMUnknown008
Something like this?

$\displaystyle \left(\begin{array}{cc}1 & 2\\ 1&2\end{array} \right).\left(\begin{array}{cc}1 & 2\\ -\frac12&-1\end{array} \right) = \left(\begin{array}{cc}0 & 0\\ 0&0\end{array} \right)$ - Nov 1st 2010, 09:31 AMjayshizwiz
No, by regular matrix i mean inverse matrix

- Nov 1st 2010, 09:36 AMUnknown008
If you multiply a matrix by its inverse you get the identity matrix...

$\displaystyle \left(\begin{array}{cc}1 & 2\\ 3&4\end{array} \right).\left(\begin{array}{cc}-2 & 1\\ \frac32&-\frac12\end{array} \right) = \left(\begin{array}{cc}1 & 0\\ 0&1\end{array} \right)$ - Nov 1st 2010, 09:57 AMjayshizwiz
I know, but that again is not my question.

Can you reach the zero matrix by multiplying an inverse square matrix with any other square matrix of the same size? (not the identity matrix, the zero matrix) - Nov 1st 2010, 09:58 AMHallsofIvy
Perhaps you mean

**invertible**matrix. If A is an invertible matrix, then the only matrix, B, such that AB= 0 is the 0 matrix itself. To see that, multiply both sides of AB= 0 by $\displaystyle A^{-1}$. - Nov 1st 2010, 10:03 AMjayshizwiz
O, lol. Shame I don't study in English... It gets in the way sometimes