Matrix A is a 3x4, matrix A times matrix B is a 3x4, what is matrix B

sorry im new to this stuff

(m x n) * (n x k) = m x k

(3 x 4) * (_ x _) = 3 x 4

First dimension of B must be the same as last dimension of A: 4
Last dimension of B must be the same as last dimension of A * B: 4

B is a 4 x 4 matrix

(3 x 4) * (4 x 4) = 3 x 4

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Similarly: (m x n) * (n x k) * (k * p) = m x p
and: (m x n) * (n x k) * (k x p) * (p x q) = m x q
etc....

Mαthmφm

A matrix of mxn size times a matrix of nxp size results in a matrix of mxp size. So, since A is 3x4, n = 4, and since AB is 3x4, p=4. So, B must be a matrix of size 4x4.

Matrix B must be a 4 by 4