Which property is shown in the matrix addition below? commutative property associative property inverse property identity property

The inverse are of two type, additive and multiplicative.

For given case, the property shown by these matrices is:

Option C: Inverse property(additive inverse and not multiplicative)

If you multiply each element of a matrix with -1, then the resultant matrix is called inverse matrix of the original matrix. It is called so because additive inverse generally means something which when added to its additive inverse add up to 0 (here 0 matrix  which is matrix  filled up with all zeroes)

For example, 2 and -2 are additive inverses. And those two matrices given are additive inverses.

Similarly there are multiplicative inverse who when multiplied with each other give 1 (for example 2 and 1/2 are multiplicative inverses)

Thus, since both the given matrices add up to zero , thus they show additive inverse property.

For given case, the property shown by these matrices is:

Option C: Inverse property(additive inverse and not multiplicative)

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Choice C) Inverse

Specifically this is the additive inverse. Note how each element adds to its corresponding pair to add to zero (eg: -6+6 = 0 in row1, column1). The additive inverse of x is the number -x. So x+(-x) = 0.