18 questions linked to/from Intuition behind Matrix Multiplication
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### Why multiplication of matrix is not done in the same way as matrix addition (i.e. adding corresponding entries)? [duplicate]

Why multiplication of matrix is not done in the same way as matrix addition (i.e. adding corresponding entries)? I know it is related to linear transformation, but by reading book I'm unable to ...
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### Why is Matrix Multiplication Not Defined Like This? [duplicate]

I'm sure everyone already thought about this at least one time. Why matrix multiplication is not defined the way showed below? \left( \begin{array}{ccc} a_{11} & a_{12} & \ldots \\ a_{21} &...
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### What does matrix multiplication have to do with scalar multiplication?

Why are matrix and scalar multiplication denoted the same way and treated as the same operation in standard mathematical notation? This is always a source of confusion for me because they have ...
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### Matrix Multiplication - Why Rows $\cdot$ Columns = Columns?

I'm nearing the end of my first year of Calculus and am pretty confident in the parts of it I've learned, yet I still don't have a good understanding of matrices, which seem like they should be easier ...
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### Is “basis times square matrix” a new basis?

Suppose we have a vector space $V = (K, +, \cdot)$. Let $B$ be a basis for $V$. Now we take an arbitrary square matrix $S \neq 0$. $BS$ is just a linear combination of $B$. Thus $BS$ should be a new ...
### show that $((GL(2,\mathbb{R}),\bullet)$ is a group
Let $G(2,\mathbb R)=\{\text{All invertible }2 \times 2\text{ matrices over }\mathbb{R}\}$. Then i want to show that $((G(2,\mathbb{R}),\bullet)$ is a group, where $\bullet$ is multiplication of ...