Question
Question: The additive inverse of a matrix A is: (a) – A (b) |A| (c) \[{{A}^{2}}\] (d) \[\dfrac{adj\t...
The additive inverse of a matrix A is:
(a) – A
(b) |A|
(c) A2
(d) ∣A∣adj A
Solution
Hint: First of all try to recollect the meaning of additive inverse of a number. That is for number n, the additive inverse is – n. Now apply the same rule to find the additive inverse of matrix A.
Complete step-by-step answer:
Here we have to find the additive inverse matrix A. Before proceeding with the question, let us know about the terms used in the question.
Additive Inverse: In mathematics, the additive inverse of a number is the number which when added to it, yields zero. This number is also known as the opposite number, sign change, or negation. For a real number, the additive inverse reverses its sign. The opposite of a positive number is negative and the opposite of a negative number is positive. Zero is the additive inverse of itself. For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of − 0.3 is 0.3, because −0.3 + 0.3 = 0. For a number, generally, the additive inverse can be calculated using multiplication by −1.
Matrix: In mathematics, a matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions that are arranged in rows and columns. The dimensions of a matrix is denoted by the number of rows and columns. For example, the dimension of the matrix below is 3 × 3 because there are three rows and three columns in it. The dimension of the matrix is read as three by three.