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When adding or subtracting matrices they must be the same dimensions. For example, if one is 2 rows and 3 columns and the other is 2 rows and 4 columns it cannot be added or subtracted so it would be no solution. However if it is 2 rows and 3 columns for both matrices they are compatible and can be added or subtracted. You notate this as 2:3.

When multiplying matrices the last number of the first matrix and the first number of the second matrix must be the same otherwise it is no solution.

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How to organize, add and multiply matrices - Bill Shillito

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Multiplication is somewhat more tricky than addition and subtraction. You first start with the first row of the first matrix and the first column of the second matrix. Match the numbers together and multiply each together. You then add the product of each. The final product is your first number. To get the second number you use the first row of the first matrix and the SECOND column of the second matrix. Multiply and add those numbers just as before. You then drop down to the second row of the first matrix and multiply it with the first column of the second matrix, then add. Then multiply the second row of the first matrix and multiply it with the second column of the second matrix, then add.

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Addition and subtraction with matrices are done the same way. You take the first number in the first column, first row in the first matrix and then add or subtract it with the first number in the second matrix. Then just match up each number of each matrix and add or subtract them to together.

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A matrix in math is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.