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Matrix multiplication is ….. Over additi...

Matrix multiplication is ….. Over addition .

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Show that addition, subtraction and multiplication are binary operations on R, but division is not a binary operation on R. Further, show that division is a binary operation on the set R^(**) of nonzero real numbers.

Show that zero is the identity for addition on R and 1 is the identity for multiplication on R. But there is no identity element for the operations - : R xx R rarr R and divid R^(*) xxR^(*) rarr R.

Explain the kinds of multiplication operations for vectors .

Show that -a is the inverse of a for the addition operation '+' on R and 1/a is the inverse of a ne0 for the multiplication operation x on R.

Show that addition and multiplication are associative binary operation on R. But subtraction is not associative on R . Division is not associative on R^(**)